Non-Linear Numerical Schemes for Exact Solutions of Initial Value Problems

In this paper, two first order convergent numerical schemes having nonlinearity in their nature have been extensively explored for their possible exact application upon initial value problems in ordinary differential equations. These two schemes have been Taylor expanded for the purpose of getting their first principal term of the local truncation error which has later been equated to zero in order to get the general form of the underlying ordinary differential equation. In this way, it has been shown that some forms of initial value problems can be obtained which produce exact solutions when these nonlinear schemes under consideration are employed on them. The obtained tabular results in the section of numerical experiments represent the exact solution obtained through the schemes. The technical computing software MAPLE 2016 running under 64-bit operating system with Windows 7 has been used to computations outputs.