A Block Integrator for the Solution of First order Ordinary Differential Equations Using Legendre...

This study established a Legendre polynomial-based block integrator for the solution of first-order ordinary differential equations. In this study, a power series as the basis function and a Legendre polynomial as a perturbation term was used. Using the multi-step collocation methodology at the grid points, four discrete approaches for step number, k = 4, have been devised. The newly built method's stability qualities were evaluated and found to be convergence. The proposed approach was shown to be useful for computing solutions to first-order ordinary differential initial value problems. The novel block methods' solutions were compared to the precise method's and other related methods' matching solutions. The implementation strategy chosen contributed to both.

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