Abstract
In this article, we implemented the Elzaki decomposition technique (EDM) to solve Volterra–Fredholm integro-differential equations of higher-order. Illustrations are used to test the technique’s accuracy and validity. Comparison among the acquired consequences by EDM and actual solutions have proven the power and accuracy of this technique. This technique is dependable and able to supply analytic remedies for solving such equations.
Highlights
Many researchers, engineers, and scientists face problems of an electrical circuit and biological species when solving differential equations resulting from the spread of heat and mass that appear with increasing and decreasing generation rates
In the early 20th century, this kind of equation was first presented by Volterra, where he studied genetic influences on population growth by developing the topic of integral and differential equations [1]
In physics, engineering, and biology applications, one can find additional details about the origins of these equations as well as the behavior of advanced integral equations [2]. e Taylor collocation, Adomian decomposition, Chebyshev, Haar wavelet, successive approximation, Bernstein, homotopy perturbation, and other technologies are widely used to work with the IDEs of higher-order [3,4,5,6,7,8,9,10,11,12,13]
Summary
Engineers, and scientists face problems of an electrical circuit and biological species when solving differential equations resulting from the spread of heat and mass that appear with increasing and decreasing generation rates. E motivation of the article is to enhance the analysis of the modified Elzaki transformation, known as the Elzaki decomposition method (EDM), to solve the higher-order IDE of Volterra–Fredholm of the form z y(n)(z) f(z) + λ1 k1(z, τ)W1(y(τ))dτ a b Special properties of the Elzaki transform are as follows.
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