What is it about?
In this study, this paper presents the construction of the four-point semiimplicit block methodicals with extra derivatives for solving y'=f(t, y). The proposed block methodicals are formulated using Hermite interpolating polynomials. the approximate solution of the problem at four points simultaneously. The block methodicals obtain the numerical solutions directly without reducing the equation into the first-order system of ordinary differential equations. The zero-stability of the proposed methodicals is also investigated.
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Why is it important?
Numerical results are presented, and comparisons with other existing block methodicals are made, the performance shows that the proposed methodicals are very efficient in solving first-order ordinary differential equations.
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This page is a summary of: A new four-points semi-implicit block method with extra derivative for solving first-order ordinary differential equations, January 2025, American Institute of Physics,
DOI: 10.1063/5.0254295.
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