A Collocation Based Block Multistep Scheme without Predictors for the Numerical Solution Parabolic Partial Differential Equations

Abstract

Introduction: Many life problems often result in differential equations models when formulated mathematically, particularly problems that depend on time and rates which give rise to Partial Differential Equations (PDE). Aims: In this paper, we advance the solution of some Parabolic Partial Dif-ferential Equations (PDE) using a block backward differentiation formula im-plemented in block matrix form without predictors. Materials and Methods: The block backward differentiation formula is devel-oped using the collocation method such that multiple time steps are evaluated simultaneously. Results: A five-point block backward differentiation formula is developed. The stability analysis of the methods reveals that the method is L0 stable. Conclusion: The implementation of some parabolic PDEs shows that the method yields better accuracy than the celebrated Crank– Nicholson’s method.