A Highly Efficient Third-Order Integrator for Initial Value Problems

Abstract

In this article, new third order well-organized numerical technique for IVP of ODE’s including partial derivative has constructed and enhanced its competency regarding truncation error. Taylor’s series is used to derive and develop new family of numerical iterative integrative. This new iterative integrator is used to evaluate numerically ODE’s with initial condition. Numerical examples are tested to check performance of each methods. Results in term of absolute error are available in each table present in this paper.  Last Absolute Error, Maximum Absolute Error and CPU Time has calculated which shows and tells proposed integrator is better in all other available methods in literature. Convergence of proposed iterative integrator method is diagnosed by testing several problems and its consequence verified with available methods. Numerical results are given for proposed METHOD to illustrate the accuracy and efficiency. The comparisons of the proposed and existing schemes having same order of local accuracy are discussed. Based on the results, the proposed iterative integrator method gives the better result than few same order methods. MATLAB 2023a is preferred for numerically and graphically analysis of methods.