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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
> Journal Vol & Issue
Journal of applied mathematics & informatics
Journal Basic Information
Journal DOI :
The Korean Society of Computational and Applied Mathematics
Editor in Chief :
Cheon-Seoung Ryoo / Hong-Tae Shim
Volume & Issues
Volume 26, Issue 5_6 - Sep 2008
Volume 26, Issue 3_4 - May 2008
Volume 26, Issue 1_2 - Jan 2008
Selecting the target year
MIXED TYPE DUALITY FOR CONTROL PROBLEMS WITH GENERALIZED INVEXITY
Husain, I. ; Ahmed, A. ; Ahmad, B. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 819~837
A mixed type dual to the control problem in order to unify Wolfe and Mond-Weir type dual control problem is presented in various duality results are validated and the generalized invexity assumptions. It is pointed out that our results can be extended to the control problems with free boundary conditions. The duality results for nonlinear programming problems already existing in the literature are deduced as special cases of our results.
SAOR METHOD FOR FUZZY LINEAR SYSTEM
Miao, Shu-Xin ; Zheng, Bing ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 839~850
In this paper, the symmetric accelerated overrelaxation (SAOR) method for solving
fuzzy linear system is discussed, then the convergence theorems in the special cases where matrix S in augmented system SX = Y is H-matrices or consistently ordered matrices and or symmetric positive definite matrices are also given out. Numerical examples are presented to illustrate the theory.
EXISTENCE OF SPANNING 4-SUBGRAPHS OF AN INFINITE STRONG TRIANGULATION
Jung, Hwan-Ok ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 851~860
A countable locally finite triangulation is a strong triangulation if a representation of the graph contains no vertex- or edge-accumulation points. In this paper we exhibit the structure of an infinite strong triangulation and prove the existence of connected spanning subgraph with maximum degree 4 in such a graph
FUZZY ERROR MATRIX IN CLSSIFICATION PROBLEMS
Kannan, S.R. ; Ramathilagam, S.R. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 861~876
This paper concerns a new method called Fuzzy Supervised Method for error matrix, the method has developed based on Adoptive Neuro- Fuzzy Inference Systems(ANFIS). For the performance point of view initially the new method tested with trial data and then this paper applies the proposed method with real world problems. So that this paper generated 1000 random error matrices in programming language [R] and then it tests the new proposed method for the error matrices. The results of Fuzzy Supervised Method given in terms of Kappa Index and Congalton Accuracy Indexes, and performance of Fuzzy Supervised Method has evaluated by using Pearson's test.
ON SOME NEW NONLINEAR DELAY AND WEAKLY SINGULAR INTEGRAL INEQUALITIES
Ma, Qing-Hua ; Debnath, L. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 877~888
This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang . Several other inequalities proved by
 and Ou-Iang  follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.
STOCHASTIC SINGLE MACHINE SCHEDULING WITH WEIGHTED QUADRATIC EARLY-TARDY PENALTIES
Zhao, Chuan-Li ; Tang, Heng-Yong ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 889~900
The problem of scheduling n jobs on a single machine is considered when the machine is subject to stochastic breakdowns. The objective is to minimize the weighted squared deviation of job completion times from a common due date. Two versions of the problem are addressed. In the first one the common due date is a given constant, whereas in the second one the common due date is a decision variable. In each case, a general form of deterministic equivalent of the stochastic scheduling problem is obtained when the counting process N(t) related to the machine uptimes is a Poisson process. It is proved that an optimal schedule must be V-shaped in terms of weighted processing time when the agreeable weight condition is satisfied. Based on the V-shape property, two dynamic programming algorithms are proposed to solve both versions of the problem.
SOME BOUNDED OPERATORS IN SPACES OF TYPE
Park, Jae-Keun ; Cho, Seong-Hoon ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 901~910
For some generalized N-function
, some Holder type inequalities and bounded operators on spaces of type
-spaces due to Pathak and Upadhyay are obtained.
AUTOMATIC NEURAL NETWORK SYSTEM FOR VORTICITY OF SQUARE CYLINDERS WITH DIFFERENT CORNER RADII
Y.El-Bakry, Mostafa. ; El-Harby, A.A. ; Behery, G.M. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 911~923
The neural networks (NNs) simulation has been designed to simulate and predict the vortex wavelength
, lateral vortex spacing
, and normalized maximum vorticity at the vortex center near the wake of square cylinders with different corner radii. The system was trained on the available data of the three cases, although this data is very little. Therefore, we designed the system to work in automatic way for finding the best network that has the ability to have the best test and prediction. The proposed system shows an excellent agreement with that of an experimental data in these cases. The technique has been also designed to simulate the other distributions not presented in the training set and predicted them with effective matching.
WEAK AND CONCRETE FILTERS OF WFI-ALGEBRAS
Jun, Young-Bae ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 925~932
The notion of weak filters in WFI-algebras is introduced. Relations between weak filters and concrete filters are established. A condition for a filter to be closed is given. Also, a condition for a filter to be a weak filter is provided. Characterizations of weak and concrete filters are discussed. A condition for a subalgebra to be a concrete filter is given.
SPECTRAL ANALYSIS OF TIME SERIES IN JOINT SEGMENTS OF OBSERVATIONS
Ghazal, M.A. ; Elhassanein, A. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 933~943
Spectral analysis of a strictly stationary r-vector valued time series is considered under the assumption that some of the observations are missed due to some random failure. Statistical properties and asymptotic moments are derived. Asymptotic normality is discussed.
Ghadiri, M. ; Waphare, B.N. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 945~959
-structures is a generalisation of both n-ary structures and
-structures. A wide class of n-ary
-groups is the n-ary
-groups that is concidered in this paper. In this paper the notion of a normal subgroup of an n-ary
-groups is introduced and the isomorphism theorems for n-ary
-groups are stated and proved. Also some examples and related properties are investigated.
ON GLOBAL EXPONENTIAL STABILITY FOR CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS
Kwon, O.M. ; Park, Ju-H. ; Lee, S.M. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 961~972
In this paper, we consider the global exponential stability of cellular neural networks with time-varying delays. Based on the Lyapunov function method and convex optimization approach, a novel delay-dependent criterion of the system is derived in terms of LMI (linear matrix inequality). In order to solve effectively the LMI convex optimization problem, the interior point algorithm is utilized in this work. Two numerical examples are given to show the effectiveness of our results.
ON THE MOMENTS OF BINARY SEQUENCES AND AUTOCORRELATIONS OF THEIR GENERATING POLYNOMIALS
Taghavi, M. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 973~981
In this paper we focus on a type of Unimodular polynomial pair used for digital systems and present some new properties of them which lead us to estimation of their autocorrelation coefficients and the moments of a Rudin-Shapiro polynomial product. Some new results on the Rudin-shapiro sequences will be presented in the last section. Main Facts: For positive integers M and n with
- 1, consider the
- M numbers
- 1) which form a collection of Rudin-Shapiro coefficients. We verify that
is dominated by
CHARACTERIZATION OF MONOIDS BY REGULAR RIGHT ACTS
Moon, Eun-Ho L. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 983~989
The purpose of this paper is to continue the investigation of monoids over which various properties of acts happen to coincide. Special concern is to characterize monoids by regular right acts. In particular there are given some characterizations of monoids over which all right acts that satisfy condition (E)(or condition (P)) are regular.
SUFFICIENCY AND DUALITY IN MINMAX FRACTIONAL SUBSET PROGRAMMING INVOLVING GENERALIZED TYPE-I FUNCTIONS
Ahmad, I. ; Sharma, Sarita ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 991~1010
A discrete minmax fractional subset programming problem is considered. Various parametric and parameter-free global sufficient optimality conditions and duality results are discussed under generalized (
)-V-type-I n-set functions.
CONDENSED CRAMER RULE FOR COMPUTING A KIND OF RESTRICTED MATRIX EQUATION
Gu, Chao ; Xu, Zhaoliang ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1011~1020
The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D,
. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for
are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation.
APPROXIMATE ANALYSIS OF AN N-DESIGN CALL CENTER WITH TWO TYPES OF AGENTS
Park, Chul-Geun ; Han, Dong-Hwan ; Baik, Kwang-Hyun ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1021~1035
In this paper, we analyze an N-design call center with skill-based routing, in which one pool of agents handles two types of calls and another pool of agents handles only one type of calls. The approximate analysis is motivated by a computational complexity that has been observed in the direct stochastic approach and numerical method for finding performance measures. The workforce staffing policy is very important to the successful management of call centers. So the allocation scheduling of the agents can be considered as the optimization problem of the corresponding queueing system to the call center. We use a decomposition algorithm which divides the state space of the queueing system into the subspaces for the approximate analysis of the N-design call center with two different types of agents. We also represent some numerical examples and show the impact of the system parameters on the performance measures.
A DIFFERENTIAL EQUATION WITH DELAY FROM BIOLOGY
Otrocol, Diana ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1037~1048
The purpose of this paper is to present a differential equation with delay from biological excitable medium. Existence, uniqueness and data dependence (monotony, continuity, differentiability with respect to parameter) results for the solution of the Cauchy problem of biological excitable medium are obtained using weakly Picard operator theory.
INTUITIONISTIC FUZZINESS OF STRONG HYPER K-IDEALS AND HYPER K-SUBALGEBRAS
Park, Chul-Hwan ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1049~1056
Intuitionistic Fuzzifications of strong hyper K-ideals and hyper K-subalgebras in hyper K-algebras are discussed, and related properties are investigated. Relations between intuitionistic fuzzy hyper K-subalgebras, intuitionistic fuzzy weak hyper K-ideals and intuitionistic fuzzy strong hyper K-ideals are provided.
AN ASYMPTOTIC FINITE ELEMENT METHOD FOR SINGULARLY PERTURBED HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS OF CONVECTION-DIFFUSION TYPE WITH DISCONTINUOUS SOURCE TERM
Babu, A. Ramesh ; Ramanujam, N. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1057~1069
We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.
INTUITIONISTIC FUZZY FILTERS OF ORDERED SEMIGROUPS
Shabir, M. ; Khan, A. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1071~1084
The notion of intuitionistic fuzzy filters in ordered semigroups is introduced and relation between intuitionistic fuzzy filters and intuitionistic fuzzy prime ideals is investegated. The notion of intuitionistic fuzzy bi-ideal subsets and intuitionistic fuzzy bi-filters are provided and relation between intuitionistic fuzzy bi-filters and intuitionistic fuzzy prime bi-ideal subsets is established. The concept of intuitionistic fuzzy right filters(1eft filters) is given and their relation with intuitionistic fuzzy prime right (left) ideals is discussed.
DOMINATION IN GRAPHS WITH MINIMUM DEGREE SIX
Jianxiang, Cao ; Minyong, Shi ; Sohn, Moo-Young ; Xudong, Yuan ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1085~1100
A set D of vertices of a graph G = (V(G),E(G)) is called a dominating set if every vertex of V(G) - D is adjacent to at least one element of D. The domination number of G, denoted by
, is the size of its smallest dominating set. Haynes et al. present a conjecture: For any graph G with
, the conjecture was proved in , , ,  and  respectively. In this paper we prove that every graph G on n vertices with
has a dominating set of order at most
. Thus the conjecture was completely proved.
FOURIER'S TRANSFORM OF FRACTIONAL ORDER VIA MITTAG-LEFFLER FUNCTION AND MODIFIED RIEMANN-LIOUVILLE DERIVATIVE
Jumarie, Guy ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1101~1121
One proposes an approach to fractional Fourier's transform, or Fourier's transform of fractional order, which applies to functions which are fractional differentiable but are not necessarily differentiable, in such a manner that they cannot be analyzed by using the so-called Caputo-Djrbashian fractional derivative. Firstly, as a preliminary, one defines fractional sine and cosine functions, therefore one obtains Fourier's series of fractional order. Then one defines the fractional Fourier's transform. The main properties of this fractal transformation are exhibited, the Parseval equation is obtained as well as the fractional Fourier inversion theorem. The prospect of application for this new tool is the spectral density analysis of signals, in signal processing, and the analysis of some partial differential equations of fractional order.
FURTHER GENERALIZATION OF OSTROWSKI'S INEQUALITY AND APPLICATIONS IN NUMERICAL INTEGRATION AND FOR SPECIAL MEANS
Xue, Qiaoling ; Liu, Wenjun ; Zhang, Wei ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1123~1132
In this paper, by introducing a parameter, we establish a new Ostrowski's integral inequality which generalizes the result of . Finally, we apply the new Ostrowski's inequality to numerical integration and special means.
OUTLIER DETECTION BASED ON A CHANGE OF LIKELIHOOD
Kim, Myung-Geun ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1133~1138
A general method of detecting outliers based on a change of likelihood by using the influence function is suggested. It can be applied to all kinds of distributions that are specified by parameters. For the multivariate normal case, specific computations are made to get the corresponding conditional influence function. A numerical example is provided for illustration.
BLIND IDENTIFICATION USING BILINEAR PAIRINGS FOR SMART CARDS
Lee, Young-Whan ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1139~1147
A. Saxena et al. first proposed a two-flow blind identification protocol in 2005. But it has a weakness of the active-intruder attack and uses the pairing operation that causes slow implementation in smart cards. In this paper, we give a method of the active-intruder attack on their identification scheme and propose a new zero- knowledge blind identification protocol for Smart cards. Our protocol consists of only two message flows and does not rely on any underlying signature or encryption scheme. The prover using computationally limited devices such as smart cards has no need of computing the bilinear pairings. It needs only for the verifier. Our protocol is secure assuming the hardness of the Discrete-Logarithm Problem in bilinear groups.
A TWO-STAGE SOURCE EXTRACTION ALGORITHM FOR TEMPORALLY CORRELATED SIGNALS BASED ON ICA-R
Zhang, Hongjuan ; Shi, Zhenwei ; Guo, Chonghui ; Feng, Enmin ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1149~1159
Blind source extraction (BSE) is a special class of blind source separation (BSS) methods, which only extracts one or a subset of the sources at a time. Based on the time delay of the desired signal, a simple but important extraction algorithm (simplified " BC algorithm")was presented by Barros and Cichocki. However, the performance of this method is not satisfying in some cases for which it only carries out the constrained minimization of the mean squared error. To overcome these drawbacks, ICA with reference (ICA-R) based approach, which considers the higher-order statistics of sources, is added as the second stage for further source extraction. Specifically, BC algorithm is exploited to roughly extract the desired signal. Then the extracted signal in the first stage, as the reference signal of ICA-R method, is further used to extract the desired sources as cleanly as possible. Simulations on synthetic data and real-world data show its validity and usefulness.
CONTROLLABILITY IN DIFFERENTIAL INCLUSIONS
Kim, Kyung-Eung ; Yang, Young-Kyun ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1161~1168
We prove a theorem that there exists at least a solution reaching the prescribed target in autonomous differential inclusion. A weak invariance theorem is obtained from this theorem as its corollary. To deduce the conclusion, we assume that the target satisfies inward pointing condition. This condition will be given by proximal normal cone.
WEIGHTED POSSIBILISTIC VARIANCE AND MOMENTS OF FUZZY NUMBERS
Pasha, E. ; Asady, B. ; Saeidifar, A. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1169~1183
In this paper, a method to find the weighted possibilistic variance and moments about the mean value of fuzzy numbers via applying a difuzzification using minimizer of the weighted distance between two fuzzy numbers is introduced. In this way, we obtain the nearest weighted point with respect to a fuzzy number, this main result is a new and interesting alternative justification to define of weighted mean of a fuzzy number. Considering this point and the weighted distance quantity, we introduce the weighted possibilistic mean (WPM) value and the weighted possibilistic variance(WPV) of fuzzy numbers. This paper shows that WPM is the nearest weighted point to fuzzy number and the WPV of fuzzy number is preserved more properties of variance in probability theory so that it can simply introduce the possibilistic moments about the mean of fuzzy numbers without problem. The moments of fuzzy numbers play an important role to estimate of parameters, skewness, kurtosis in many of fuzzy times series models.
ON NEW IDENTITIES FOR 3 BY 3 MATRICES
Lee, Woo ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1185~1189
In this paper we show that the polynomial of degree 9 called generalized algebraicity is a polynomial identity for
MULTIPLE SCALE ANALYSIS OF A DELAYED PREDATOR PREY MODEL WITHIN RANDOM ENVIRONMENT
Saha, Tapan ; Bandyopadhyay, Malay ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1191~1205
We consider a delayed predator prey model. The local stability and Hopf bifurcation results are stated taking the time delay as a control parameter. We apply multiple scale analysis to analyze the effects of additive white noises near the Hopf bifurcation point at the positive interior equilibrium state. The governing equations for the amplitude of oscillations on a slow time scale are derived. We identify the process of amplitude of oscillations and derive its transient properties. We show that oscillations, which would decay in the deterministic system whenever time delay lies below its critical value, persists for long time under the validity of multiple scale analysis.
OBLIQUE PROJECTIONS AND SHIFT-INVARIANT SPACES
Park, Sang-Don ; Kang, Chul ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1207~1214
We give an elementary proof of one of the main results in [H.O. Kim, R.Y. Kim, J.K. Lim, The infimum cosine angle between two finitely generated shift-invariant spaces and its applications, Appl. Comput. Har-mon. Anal. 19 (2005) 253-281] concerning the existence of an oblique projection onto a finitely generated shift-invariant space along the orthogonal complement of another finitely generated shift-invariant space under the assumption that the generators generate Riesz bases.
PRIME FACTORS OF
Shin, Yong-Su ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1215~1219
We find a necessary and sufficient condition that the prime factors of
coincide for odd positive integers
. Moreover, we also find a necessary and sufficient condition that the set of all prime factors of
is a subset of those of
VAGUE SET THEORY BASED ON d-ALGEBRAS
Lee, Kyoung-Ja ; Kim, Young-Hee ; Cho, Yong-Uk ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1221~1232
The notions of vague d-subalgebras, vague BCK-ideals, vague d-ideals, vague
-ideals and vague
-ideals are introduced, and their properties are investigated. Relations between vague d-subalgebras, vague BCK-ideals, vague d-ideals, vague
-ideals and vague
-ideals are established.
AN ITERATIVE ALGORITHM FOR SOLVING THE LEAST-SQUARES PROBLEM OF MATRIX EQUATION AXB+CYD=E
Shen, Kai-Juan ; You, Chuan-Hua ; Du, Yu-Xia ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1233~1245
In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB+CYD=E over unknown matrix pair [X, Y]. By this iterative method, for any initial matrix pair [
], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [
] in Frobenius norm. Given numerical examples show that the algorithm is efficient.
TIGHT MATRIX-GENERATED GABOR FRAMES IN
WITH DESIRED TIME-FREQUENCY LOCALIZATION
Christensen, Ole ; Kim, Rae-Young ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1247~1256
Based on two real and invertible
matrices Band C such that the norm
is sufficiently small, we provide a construction of tight Gabor frames
with explicitly given and compactly supported generators. The generators can be chosen with arbitrary polynomial decay in the frequency domain.
ON DUALITY THEOREMS FOR CONVEXIFIABLE OPTIMIZATION PROBLEMS
Kim, Moon-Hee ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1257~1261
In this paper, we consider of a convexifiable programming problem with bounds on variables. We obtain Mond-Weir type duality theorems for the convexifiable programming problems. Moreover, we give a numerical example to illustrate our duality.
SOME LOCAL SPECTRAL PROPERTIES OF T AND S WITH AT - SA = 0
Yoo, Jong-Kwang ; Han, Hyuk ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1263~1272
Let T and S be bounded linear operators on Banach spaces X and y, respectively. A linear map A : X
y is said to be an intertwiner if AT - SA = 0. In this paper we study the relation between local spectral properties of T and S on the assumption of AT - SA = 0. We give some example of intertwiner with T and S.
NUMERICAL INTEGRATION METHOD FOR SINGULAR PERTURBATION PROBLEMS WITH MIXED BOUNDARY CONDITIONS
Andargie, Awoke ; Reddy, Y.N. ;
Journal of applied mathematics & informatics, volume 26, issue 5_6, 2008, Pages 1273~1287
In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.