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.
ABBASZADE, M., & MOHEBBI, M. (2012). Fourth-order Numerical Solution of a Fractional PDE with the Nonlinear Source Term in the Electroanalytical Chemistry. Iranian Journal of Mathematical Chemistry, 3(2), 195-220. doi: 10.22052/ijmc.2012.5147
MLA
M. ABBASZADE; M. MOHEBBI. "Fourth-order Numerical Solution of a Fractional PDE with the Nonlinear Source Term in the Electroanalytical Chemistry". Iranian Journal of Mathematical Chemistry, 3, 2, 2012, 195-220. doi: 10.22052/ijmc.2012.5147
HARVARD
ABBASZADE, M., MOHEBBI, M. (2012). 'Fourth-order Numerical Solution of a Fractional PDE with the Nonlinear Source Term in the Electroanalytical Chemistry', Iranian Journal of Mathematical Chemistry, 3(2), pp. 195-220. doi: 10.22052/ijmc.2012.5147
VANCOUVER
ABBASZADE, M., MOHEBBI, M. Fourth-order Numerical Solution of a Fractional PDE with the Nonlinear Source Term in the Electroanalytical Chemistry. Iranian Journal of Mathematical Chemistry, 2012; 3(2): 195-220. doi: 10.22052/ijmc.2012.5147
)