Numerical solution of fractional partial differential equations via Haar wavelet

Abstract

AbstractHaar wavelet collocation method is applied for the numerical solution of fractional partial differential equations. The proposed method is first applied to one‐dimensional fractional partial differential equations and then it is extended to higher‐dimensional fractional partial differential equations as well. Both time‐fractional as well as space–time‐fractional partial differential equations are considered. The fractional order derivatives involved are evaluated using the Caputo definition. The proposed method is semi‐analytic as it involves exact integration of Caputo derivative. The proposed method is widely applicable and robust. The method is tested upon several test problems. The results are computed and presented in the form of maximum absolute errors. The numerical tests confirm the accuracy, efficiency and simple applicability of the proposed method.