On the Convergence and Stability of Finite Difference Method for Parabolic Partial Differential Equations
B. J. Omowo *
Department of Mathematics, Nasarawa State University, Keffi, Nigeria.
I. O. Longe
Department of Statistics, Federal Polytechnic, Ile-Oluji, Nigeria.
C. E. Abhulimen
Department of Mathematics, Ambrose Ali University, Ekpoma, Nigeria.
H. K. Oduwole
Department of Mathematics, Nasarawa State University, Keffi, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Finite difference scheme, Crank-Nicolson scheme, stability, modifed Crank-Nicolson scheme, diffusion equations.