Spline solution of the generalized Burgers'-Fisher equation

Abstract

A numerical method based on exponential spline and finite difference approximations is developed to solve the generalized Burgers'-Fisher equation. The error analysis, stability and convergence properties of the method are studied via energy method. The method is shown to be unconditionally stable and accurate of orders 𝒪(k + kh + h ²) and 𝒪(k + kh + h ⁴). Some test problems are given to demonstrate the applicability of the purposed method numerically. Numerical results verify the theoretical behaviour of convergence properties. The main superiority of the presented scheme is its simplicity and applicability in comparison with the existing well-known methods.

Keywords:

• generalized Burgers'-Fisher equation
• exponential spline
• finite difference
• convergence
• energy method

AMS Subject Classifications:

• 65L10
• 65M06
• 65M12