• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.131-145
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• 2013

In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.87-97
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• 2013

The purpose of this paper is to employ a new useful technique to solve the initial-Neumann boundary value problems for parabolic, hyperbolic and parabolic-hyperbolic equations and obtain a solution in form of infinite series. The results obtained indicate that this approach is indeed practical and efficient.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.331-348
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• 2018

In this paper, an initial value method for solving a class of singularly perturbed delay differential equations with layer behavior is proposed. In this approach, first the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay using Taylor series expansion. Then from the modified problem, two explicit Initial Value Problems which are independent of the perturbation parameter, ${\varepsilon}$, are produced: the reduced problem and boundary layer correction problem. Finally, these problems are solved analytically and combined to give an approximate asymptotic solution to the original problem. To demonstrate the efficiency and applicability of the proposed method three linear and one nonlinear test problems are considered. The effect of the delay on the layer behavior of the solution is also examined. It is observed that for very small ${\varepsilon}$ the present method approximates the exact solution very well.

• 대한조선학회논문집
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• 제43권6호
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• pp.683-692
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• 2006

The BEM, known as solving boundary value problems, could have some advantages In solving domain problems which are mostly solved by FEM and FDM. Lately, in the elastic-plastic nonlinear problems, BEM could provide the subdomain approach for the region where the plastic deformation could occur and the unknown nodal displacement of this region are added as the unknown of the boundary integral equation for this approach. In this paper, initial stress method was used to establish the formulation of such BEM approach. And a simple rectangular plate having a circular hole was analyzed to verify the suggested method and the result is compared with that from FEM. It is shown that the result of two methods are showing similar stress-strain curves at the root of perforated plate and furthermore the plastic deformation obtained by BEM shows more reasonable behavior than that of FEM.

• 대한수학회논문집
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• 제24권4호
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• pp.605-615
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• 2009

In this paper, we develop a reliable algorithm which is called the variation of parameters method for solving sixth-order boundary value problems. The proposed technique is quite efficient and is practically well suited for use in these problems. The suggested iterative scheme finds the solution without any perturbation, discritization, linearization or restrictive assumptions. Moreover, the method is free from the identification of Lagrange multipliers. The fact that the proposed technique solves nonlinear problems without using the Adomian's polynomials can be considered as a clear advantage of this technique over the decomposition method. Several examples are given to verify the reliability and efficiency of the proposed method. Comparisons are made to reconfirm the efficiency and accuracy of the suggested technique.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.215-222
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• 2000

A multigrid algorithm is developed for solving the one- dimensional initial boundary value problem. The numerical solutions of linear and nonlinear Burgers; equation for various initial conditions are studied. The stability conditions are derived by Von -Neumann analysis . Numerical results are presented.

• Structural Engineering and Mechanics
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• 제68권6호
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• pp.713-720
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• 2018

In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results.

• 대한수학회보
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• 제34권1호
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• pp.135-146
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• 1997

For the numerical simulation of wave phenomena either in unbounded domains that it is not feasible to compute solutions on the entire region, it is needed to truncate the original domains to manageable bounded domains whose geometries are simple but usually nonsmooth. On the artificial boundaries thus created, absorbing boundary conditions are taken so that the significant part of waves arriving at the artificial boundaries can be transmitted [5,10,11,16,17,26]$.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1265-1277
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• 2009

In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.