Integral Equations

doi:10.3390/books978-3-0365-2239-5

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Integral Equations

Theories, Approximations and Applications

Edited by

October 2021

208 pages

ISBN978-3-0365-2240-1 (Hardback)
ISBN978-3-0365-2239-5 (PDF)

https://doi.org/10.3390/books978-3-0365-2239-5

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This book is a reprint of the Special Issue Integral Equations: Theories, Approximations and Applications that was published in

Biology & Life Sciences

Chemistry & Materials Science

Computer Science & Mathematics

Physical Sciences

Summary

Linear and non-linear integral equations of the first and second kinds have many applications in engineering and real life problems. Thus, we try to find efficient and accurate methods to solve these problems. The aim of this editorial is to overview the content of the Special Issue “Integral Equations: Theories, Approximations and Applications”.This Special Issue collects innovative contributions addressing the top challenges in integral equations, integro-differential equations, multi-dimensional problems, and ill-posed and singular problems with modern applications. It covers linear and non-linear integral equations of the first and second kinds, singular and ill-posed kernels, system of integral equations, high-dimensional problems, and especially new numerical, analytical, and semi-analytical methods for solving the problems mentioned by focusing on modern applications.

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Keywords

(ϕ, ψ)-metric space; topological property; fixed point; Fredholm integral equation; stochastic arithmetic; homotopy perturbation method; CESTAC method; CADNA library; Volterra integral equation with piecewise continuous kernel; hydrogen; natural gas; gas mixture; homotopy analysis method; method of characteristics; reduced order modelling; leak locations; matrix expression of convolution; Laplace-type transforms; convolution neural network; kernel; weakly singular Volterra integral equations; Picard iteration; product integration; numerical approximation; nonlinear Volterra integral equation; weakly singular kernels; Abel’s integral equations; the Genocchi polynomials; operational matrix; nanofluid; second-order slip velocity; nanoparticles migration; homotopy analysis method; backward doubly stochastic differential equations; stochastic differential game; maximum principle; Nash equilibrium point; time-delayed generator; non-equilibrium heat transfer problem; time-dependent response function; second-kind integro-differential equations; Volterra integral equations; Volterra integral equation; multistep method with constant coefficients; degree and stability; advanced multistep methods; hybrid method; multistep second derivative methods; necessary condition for the convergency; Fredholm–Volterra integral equations; fixed-point theorems; numerical approximations; n/a