Open AccessNumerical Solution of Two-Parameter Singularly Perturbed Convection-Diffusion Boundary Value Problems via Fourth Order Compact Finite Difference Method
Author(s) -
Ram Kishun Lodhi,
Bharat Raj Jaiswal,
Durgesh Nandan,
K. Ramesh
Publication year - 2021
Publication title -
mathematical modelling and engineering problems/mathematical modelling of engineering problems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.26
H-Index - 11
eISSN - 2369-0747
pISSN - 2369-0739
DOI - 10.18280/mmep.080519
Subject(s) - compact finite difference , mathematics , tridiagonal matrix , finite difference method , boundary value problem , numerical analysis , finite difference , convergence (economics) , numerical solution of the convection–diffusion equation , mathematical analysis , finite element method , mixed finite element method , eigenvalues and eigenvectors , physics , quantum mechanics , economics , thermodynamics , economic growth
In this study, we have developed a fourth order compact finite difference method for finding the numerical solution of two-parameter singularly perturbed convection-diffusion boundary value problems. We have used fourth order compact finite difference method on uniform mesh which provides a tridiagonal linear system of equations. The convergence analysis of the proposed method is established through a matrix analysis approach and it is proved that present method gives fourth order convergence results. Present method is implemented on two numerical examples for checking the efficiency and precision of the method. Numerical outcomes are exhibited which supports the theoretical outcomes. Numerical outcomes are compared with other existing methods and found that present method gives more accurate approximate solution as compare to the other existing methods.