fourth-order numerical solution of a fractional pde with the nonlinear source term in the electroanalytical chemistry

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the riemann-liouville derivative to obtain a fully discrete implicit scheme and analyze the solvability, stability and convergence of proposed scheme using the fourier method. the convergence order of method is o(t + n4). numerical examples demonstrate the theoretical results and high accuracy of proposed scheme.