Haar 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.
In this article, Haar wavelet collocation technique is adapted to acquire the approximate solution of fractional Korteweg‐de Vries (KdV), Burgers', and KdV–Burgers' equations. The fractional order derivatives involved are described using the Caputo definition. In the proposed technique, the given nonlinear fractional differential equation is discretized with the help of Haar wavelet and reduced to the nonlinear system of equations, which are solved with Newton's or Broyden's method. The proposed method is semi‐analytic as it involves exact integration of Caputo derivative. The proposed technique is widely applicable and robust. The technique is tested upon many test problems. The results are computed and presented in the form of maximum absolute errors which show the accuracy, efficiency, and simple applicability of the proposed method.
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