2022•Polytechnic JournalOpen access

Iterative Kernel Technique to Solve System Fredholm Integral Equation First Kind for Degenerate Kernel

Talhat I. Hassan

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Abstract

Many problems associated with the engineering technology field can be transformed into Fredholm integral equations of the first kind to achieve problem-solving strategies. In this paper, the iterative kernel technique was reformulated to treat the numerical solution for the system of Fredholm integral equations of the first kind for the degenerate kernel. Three new theorems have been proposed and proved. This technique was programmed via Matlab and achieved a good result.

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Many problems associated with the engineering technology field can be transformed into Fredholm integral equations of the first kind to achieve problem-solving strategies. In this paper, the iterative kernel technique was reformulated to treat the numerical solution for the system of Fredholm integral equations of the first kind for the degenerate kernel. Three new theorems have been proposed and proved. This technique was programmed via Matlab and achieved a good result.

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Available abstract

Many problems associated with the engineering technology field can be transformed into Fredholm integral equations of the first kind to achieve problem-solving strategies. In this paper, the iterative kernel technique was reformulated to treat the numerical solution for the system of Fredholm integral equations of the first kind for the degenerate kernel. Three new theorems have been proposed and proved. This technique was programmed via Matlab and achieved a good result.

Key concepts: Fredholm integral equation, Kernel (algebra), Integral equation, Degenerate energy levels, Fredholm theory, Mathematics, Iterative method, Applied mathematics

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