A Taylor-type numerical method for solving nonlinear ordinary differential equations

A novel approximate method is proposed for solving nonlinear differential equations. Chang and Chang in [8] suggested a technique for calculating the one-dimensional differential transform of nonlinear functions. In this paper, we introduce new polynomials based on differential transform method (DTM), which is a Taylor series method in essence. Due to this, the new method falls in the wide category of Taylor-type iterative methods. The presented method proposes a new algorithm for computing the transformed function with all forms of nonlinearities. The proofs of the main results will also be furnished. The reliability and efficiency of the method are illustrated by investigating the convergence results for some nonlinear differential equations. In fact, comparisons are made between the contributed scheme and the generated results of MATLABbvp4c. The numerical results uphold the theoretical aspects.