Abstract
In this paper, the two-dimensional Bernoulli wavelets (BWs) with Ritz–Galerkin method are applied for the numerical solution of the time fractional diffusion-wave equation. In this way, a satisfier function which satisfies all the initial and boundary conditions is derived. The two-dimensional BWs and Ritz–Galerkin method with satisfier function are used to transform the problem under consideration into a linear system of algebraic equations. The proposed scheme is applied for numerical solution of some examples. It has high accuracy in computation that leads to obtaining the exact solutions in some cases.
Highlights
Many phenomena in various field of the science, can be modeled very successfully by time-fractional differential equations
In this paper we focus on the following fractional diffusion-wave equation (FDWE) with damping [1]: oquðx; otq tÞ
Chen et al [1] obtained the analytical solution by the method of separation of variables and proposed the numerical solution with finite difference method
Summary
Many phenomena in various field of the science, can be modeled very successfully by time-fractional differential equations. 3t2ex t3ex: The initial and boundary conditions are determined correspondingly to the exact solution uðx; tÞ 1⁄4 ext: From (3.18), we obtain wðx; tÞ 1⁄4 t3ð1 À x þ exÞ, apply the numerical method presented in this paper for k1 1⁄4 k2 1⁄4 1 and M1 1⁄4 M2 1⁄4 3. Liu et al [3] employed the fractional predictor–corrector method and solved this problem with q 1⁄4 1:85 and different values of time and space step sizes They obtained 1:6341 Â 10À3 for the best maximum absolute error. 0 7:07305E À 11 3.82387EÀ10 2.504EÀ9 7.99214EÀ9 5.66433EÀ10 2.76078EÀ8 4.00415EÀ8 1.23163EÀ8 6.36963EÀ8 0 0.405
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