Two{step fourth{order TC scheme for solving time{dependent equations

This paper presents the numerical technique for solving one of the most well-known time{ dependent equation. This scheme includes collocation method with Legendre wavelets for spatial discretization and Two{step fourth-order Taylor method for time discretization. In contrast with the Taylor collocation method the present scheme does not contain any new higher-order derivatives. Some numerical examples are given and compared with the one{step TC method. The obtained results show that the proposed method is more accurate and stable.