Exponential finite difference methods for solving Newell–Whitehead–Segel equation
Nayrouz Hilal, Sami Injrou, Ramez Karroum
Abstract
Abstract 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.
Topics & Concepts
MathematicsExponential functionFinite differenceConsistency (knowledge bases)Applied mathematicsFinite difference methodNonlinear systemPartial differential equationFinite difference coefficientWork (physics)Mathematical analysisFinite element methodMixed finite element methodDiscrete mathematicsMechanical engineeringQuantum mechanicsPhysicsThermodynamicsEngineeringMathematical Biology Tumor GrowthFractional Differential Equations SolutionsNumerical methods for differential equations