An Efficient Chebyshev Wavelet Collocation Technique for the Time-Fractional Camassa-Holm Equation

Abstract

By employing the third-order Chebyshev collocation technique along with relevant wavelets, we tackle a third-order singular fractional partial differential equation (PDE). We directly build the Chebyshev operation matrix of the third kind, avoiding the use of the block-pulse function or any approximations. To reduce the order of equation in this approach, we transform the higher-order PDEs into a system of PDEs. Next, we utilize the third-kind Chebyshev wavelet collocation method to convert the resulting system from the prior step into a set of algebraic equations. To demonstrate the method's effectiveness, we apply it to the time-fractional Camassa-Holm equation and a third-order time-singular PDE. The outcomes are compared with those from several established methods to illustrate the method's efficiency and practicality.