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ORIGINAL PAPER
An Extended Finite Difference Method for Singular Perturbation Problems on a Non-Uniform Mesh
1
Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, Telangana, India
2
Department of Mathematics, University College for Women, Kakatiya University, Warangal, Telangana, India
Online publication date: 2022-03-17
Publication date: 2022-03-01
International Journal of Applied Mechanics and Engineering 2022;27(1):203-214
KEYWORDS
ABSTRACT
An extended second order finite difference method on a variable mesh is proposed for the solution of a singularly perturbed boundary value problem. A discrete equation is achieved on the non uniform mesh by extending the first and second order derivatives to the higher order finite differences. This equation is solved efficiently using a tridiagonal solver. The proposed method is analysed for convergence, and second order convergence is derived. Model examples are solved by the proposed scheme and compared with available methods in the literature to uphold the method.
REFERENCES (15)
1.
Bigge J. and Bohl E. (1985): Deformations of the bifurcation diagram due to discretisation.– Math. Comput., vol.45, pp.393-403.
2.
Ackerberg R.C. and O’Malley R.E. (1970): Boundary layer problems exhibiting resonance.– Stud. Appl. Math., vol.49, pp.277-295.
3.
Ardema M.D. (1983): Singular Perturbations in Systems and Control.– Springer-Verlag, New York.
4.
Mohammadi R. (2012): Numerical solution of general singular perturbation boundary value problems based on the Adaptive cubic spline.– TWMS Jour. Pure Appl. Math., vol.3, pp.11-21.
5.
Pooja K. and Arshad K. (2017): Singularly perturbed convection-diffusion boundary value problems with two small parameters using non-polynomial spline technique.– Math. Sci., vol.11, pp.119-126.
6.
Kadalbajoo M.K. and Bawa R.K. (1996): Variable mesh difference scheme for singularly-perturbed boundary-value problems using splines.– J. Optim. Theory Appl., vol.90, pp.405-416.
7.
Surla K., Uzelac Z. and Teofanov L.(2009): The discrete minimum principle for quadratic spline discretization of a singularly perturbed problem.– Mathematics and Computers in Simulation, vol.79, pp. 2490-2505.
8.
Doolan E.P., Miller J.J.H. and Schilders W.H.A. (1980): Uniform Numerical Methods for Problems with Initial and Boundary Layers.– Boole Press, Dublin.
9.
Kadalbajoo M.K., Sharma K.K. (2008): A numerical method based on the finite difference for boundary value problems for singularly perturbed delay differential equations.– Mathematics and Computers in Simulation, vol.197, pp.692-707.
10.
Hemker P.W. and Miller J.J.H. (1979): Numerical Analysis of Singular Perturbation Problem.– Academic Press, New York.
11.
Kadalbajoo M.K. and Patidar K.C. (2003): Spline approximation method for solving self-adjoint singular perturbation problems on non-uniform grids.– J. Comput. Anal. Appl., vol.5, pp.425-451.
12.
O’Malley R.E. (1974): Introduction to Singular Perturbations.– Academic Press, New York.
13.
Miller J.J.H., O’Riordan E. and Shishkin G.I. (1996): Fitted Numerical Methods for Singular Perturbation Problems.– World Scientific, Singapore.
14.
Aziz T. and Khan A. (2002): A spline method for second order singularly perturbed boundary-value problems.– J. Comput. Appl. Math., vol.147, pp.445-452.
15.
Kadalbajoo M.K. and Patidar K.C. (2006): ɛ -Uniformly convergent fitted mesh finite difference methods for general singular perturbation problems.– Appl. Math. Comput., vol.179, pp.248-266.
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