Open AccessOn the Convergence and Stability of Finite Difference Method for Parabolic Partial Differential Equations
Author(s) -
B. J. Omowo,
I. O. Longe,
C. E. Abhulimen,
H. K. Oduwole
Publication year - 2021
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2021/v36i1030412
Subject(s) - convergence (economics) , stability (learning theory) , mathematics , consistency (knowledge bases) , scheme (mathematics) , partial differential equation , finite difference , finite difference scheme , finite difference method , mathematical analysis , computer science , geometry , machine learning , economics , economic growth
In this paper, we verify the convergence and stability of implicit (modified) finite difference scheme. Knowing fully that consistency and stability are very important criteria for convergence, we have prove the stability of the modied implicit scheme using the von Newmann method and also verify the convergence by comparing the numerical solution with the exact solution. The results shows that the schemes converges even as the step size is rened.