Abstract:
The main focus of our work is to present a survey of generalized Runge-Kutta integrals (RK, RKN, RKD, RKT, RKFD, RKTF, and RKM) to solve for first, second, third, fourth, fifth, seventh- even tenth order. Ordinary differential equations for the development of RK-type explicit direct integration tools for the solution of computational development equations are the major contributions of these papers. To solve the generalized RK equations to solve the ODE equations, the order terms (OCs) of the proposed integrators are derived using Taylor expansion, direct numerical methods with different phases are derived based on these conditions, . Some implementation computation methods are also tested to show the new methods are compatible with the existing RK methods and save a large amount of computational time and require less functional evaluations. The use of modern scientific programs and systems such as MATLAB and MAPEL has the most important role in our study.
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