University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 3 2 2012 09 01 Fourth-order Numerical Solution of a Fractional PDE with the Nonlinear Source Term in the Electroanalytical Chemistry 195 220 5147 10.22052/ijmc.2012.5147 EN M. ABBASZADE University of Kashan, Kashan, I. R. Iran M. MOHEBBI University of Kashan, Kashan, I. R. Iran Journal Article 2012 05 13 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. https://ijmc.kashanu.ac.ir/article_5147_55d4072ecb915e23ccc789254cf387c2.pdf