Numerical study of the nonlinear Cauchy diusion problem and Newell-Whitehead equation via cubic B-spline quasi-interpolation

In this article, a numerical approximation to the solution of the Newell- Whitehead equation (NWE) and Cauchy problem of ill-posed non-linear dif- fusion equation have been studied. The presented scheme is obtained by using the derivative of the cubic B-spline quasi-interpolation (BSQI) to ap- proximate the spatial derivative of the dependent variable and rst order forward dierence to approximate the time derivative of the dependent vari- able. Some numerical experiments are provided to illustrate the method. The results of numerical experiments are compared with analytical solutions. The main advantage of the scheme is that the algorithm is very simple and very easy to implement.