Exponential finite difference methods for solving Newell-Whitehead-Segel equation. (English) Zbl 1442.65160

Summary: This work presents two different finite difference methods to compute the numerical solutions for Newell-Whitehead-Segel partial differential equation, which are implicit exponential finite difference method and fully implicit exponential finite difference method. Implicit exponential methods lead to nonlinear systems. Newton method is used to solve the resulting systems. Stability and consistency are discussed. To illustrate the accuracy of the proposed numerical methods, some examples are delivered at the end.


65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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