The aim of the study is to obtain the numerical solution of first initial boundary value problem (IBVP) for semi-linear variable order fractional diffusion equation by using different finite difference schemes. We developed the three finite difference schemes namely explicit difference scheme, implicit difference scheme and Crank-Nicolson difference scheme, respectively for variable order type semi-linear diffusion equation. For this scheme the stability as well as convergence are studied via Fourier method. At the end, solution of some numerical examples are discussed and represented graphically using Matlab.
Birajdar, Gunvant A. and Rashidi, M. M.
Finite Difference Schemes for Variable Order Time-Fractional First Initial Boundary Value Problems,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 12,
1, Article 8.
Available at: https://digitalcommons.pvamu.edu/aam/vol12/iss1/8