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Taylor collocation method for a system of nonlinear Volterra delay integro-differential equations with application to COVID-19 epidemic

, 2020
Laib H, Bellour A, Boulmerka A.
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Modified HAM for solving linear system of Fredholm-Volterra Integral Equations

Malaysian Journal of Mathematical Sciences, 2022
This paper considers systems of linear Fredholm-Volterra integral equations using a modified homotopy analysis method (MHAM) and the Gauss-Legendre quadrature formula (GLQF) to find approximate solutions. Standard homotopy analysis method (HAM), MHAM, and optimal homotopy asymptotic method (OHAM) are compared for the same number of iterations.
Eshkuvatov, Z. K., Ismail, Sh., Mamatova, H. X., Viscarra, D. S., Aloev, R. D.   +4 more
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Numerical approach for nonlinear system of Fredholm-Volterra integral equations

AIP Conference Proceedings, 2021
In this note, the homotopy analysis method (HAM) is applied as a tool for solving the system of non-linear Fredholm-Volterra integral equations. The generalized chain rule is implemented for differentiation of the non-linear kernel functions with many variables, and the non-linear problem is reduced into a sequence of known non-linear integral equa ...
Zainidin Eshkuvatov, Husnida Mamatova, Shahrina Ismail, Ilyani Abdullah, Rakhmatillo Aloev   +4 more
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Fredholm–Volterra integral equation in contact problem

Applied Mathematics and Computation, 2003
The author considers the Fredholm-Volterra integral equation \[ kP(x,y,t)+q\int\limits_0^\infty\int\limits_0^\infty \frac{P(\xi,\eta,t)\,d\xi\,d\eta}{\sqrt{(x-\xi)^2+(y-\eta)^2}} +q\int\limits_0^t F(t,\tau)P(x,y,\tau) \,d\tau=f(x,y,t) \tag{1} \] in the space \(L_2(\Omega)\times C(0,T)\), under the condition \[ \int\limits_0^\infty\int\limits_0^\infty P(
Abdou, M. A., Moustafa, Osama L.
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On the numerical solutions of Fredholm–Volterra integral equation

Applied Mathematics and Computation, 2003
The authors describe the Toeplitz matrix method and the product Nystrom method for the mixed Fredholm-Volterra singular integral equation of the second kind: \[ \mu\phi(x,t)-\lambda\int_{-1}^1k(x,y)\phi(y,t)\,dy- \lambda\int_0^tF(t, \tau)\phi(x,\tau)\,d\tau= f(x,t),\quad 0\leqslant t\leqslant T,\;| x| \leqslant1,\tag{1} \] where \(k\), \(F\) and \(f ...
Abdou, M. A., Mohamed, Khamis I., Ismail, A. S.   +2 more
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Fredholm–Volterra integral equation with singular kernel

Applied Mathematics and Computation, 2003
The author considers the Fredholm-Volterra integral equation of the second kind \[ \delta\phi(x,t)+\int\limits_{-1}^1 \left| \ln| y-x| -d\right| \phi(y,t)\,dy+\int\limits_0^t F(\tau)\phi(x,\tau) \,d\tau=f(x,t),\tag{1} \] where \(| x| \leq1,\) \( t\in[0,T],\) \(\lambda\in(0,\infty),\) \(\delta\in(0,\infty]\), with a specific right-hand side \(f(x,t ...
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Chelyshkov Collocation Method for Solving the Two-Dimensional Fredholm–Volterra Integral Equations

International Journal of Applied and Computational Mathematics, 2017
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Ardabili, J. Saffar, Talaei, Y.
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Fredholm–Volterra integral equation and generalized potential kernel

Applied Mathematics and Computation, 2002
For a Fredholm integral equation of the first and second kind explicit solutions are obtained for the kernel function \[ K(x,y)=\sqrt{xy}\int_0^\infty \lambda^\alpha J_n(x\lambda)J_n(y\lambda) d\lambda. \] Here, \(J_n\) is a Bessel function of the first kind.
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