Approximate solutions of nonlinear Volterra integral equations of the first kind

Kasumo, Christian; Moyo, Edwin

doi:10.12988/ams.2020.914288

Cited by 2 publications

(1 citation statement)

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“…In this article, the focus of our attention is on the numerical solution of ( 1 ) based on the block-by-block method. In Kasumo and Moyo ( 2020 ), the others have constructed a numerical method using this block-by-block method. They built it in two main steps: linearization of the equation ( 1 ) and then descritisation by the block-by-block method fourth order.…”

Section: Introductionmentioning

confidence: 99%

Block-by-block method for solving non-linear Volterra integral equation of the first kind

Ghiat

Tair²,

Ghuebbai³

et al. 2023

Comp. Appl. Math.

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In this paper, we focus on the numerical solution of the non-linear Volterra integral equation of the first kind. We start by converting its form to a second-kind Volterra equation and we construct some assumptions to give a sufficient condition to ensure the solution’s existence and uniqueness, this is on the one hand. On the other hand, to use it in the numerical and analytical analysis computation which put the two analyses compatible. Then, by applying block-by-block method, we transform our integral equation to a non-linear system. This system gives us a discrete numerical solution converging to our analytical solution. The approximate solution is computed using a Newton’s method and the numerical examples clearly demonstrate the efficiency of our proposed method compared with the Nystöm method.

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Section: Introductionmentioning

confidence: 99%