A new coupled wavelet-based method applied to the nonlinear reaction–diffusion equation arising in mathematical chemistry

In this paper, we have applied the wavelet-based coupled method for finding the numerical solution of Murray equation. To the best of our knowledge, until now there is no rigorous Legendre wavelets solution has been reported for the Murray equation. The highest derivative in the differential equation is expanded into Legendre series, this approximation is integrated while the boundary conditions are applied using integration constants. With the help of Legendre wavelets operational matrices, the Murray equation is converted into an algebraic system. Block pulse functions are used to investigate the Legendre wavelets coefficient vectors of nonlinear terms. The convergence of the proposed method is proved. Finally, we have given a numerical example to demonstrate the validity and applicability of the method. Moreover the use of proposed wavelet-based coupled method is found to be simple, efficient, less computation costs and computationally attractive.