Periodic solutions of Volterra integral equations by M. N. Islam

Subjects: “…Volterra integral equation…”
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On Some Classes of Linear Volterra Integral Equations by Anatoly S. Apartsyn

“…The sufficient conditions are obtained for the existence and uniqueness of continuous solution to the linear nonclassical Volterra equation that appears in the integral models of developing systems. The Volterra integral equations of the first kind with piecewise smooth kernels are considered. …”
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Approximation approach for backward stochastic Volterra integral equations by Kutorzi Edwin Yao, Mahvish Samar, Yufeng Shi

“…In this paper, we focus on studying a specific type of equations called backward stochastic Volterra integral equations (BSVIEs). Our approach to approximating an unknown function involved using collocation approximation. …”
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On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation by H. S. Mamba, M. Khumalo

“…We consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. …”
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Sawi Decomposition Method for Volterra Integral Equation with Application by M. Higazy, Sudhanshu Aggarwal, Taher A. Nofal

“…In this paper, authors present a new method “Sawi decomposition method” for determining the primitive of Volterra integral equation (V.I.E.) with application. Sawi decomposition method is the combination of Sawi transformation and decomposition method. …”
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Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems by M. I. Berenguer, D. Gámez, A. I. Garralda-Guillem, M. C. Serrano Pérez

“…We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. …”
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New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations by İhsan Timuçin Dolapçı, Mehmet Şenol, Mehmet Pakdemirli

“…In this paper, recently developed perturbation iteration method is used to solve Fredholm and Volterra integral equations. The study shows that the new method can be applied to both types of integral equations. …”
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Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments by Mahdi Namazi Nezamabadi, Saeed Pishbin

“…In this paper, we use the operational Tau method based on orthogonal polynomials to achieve a numerical solution of generalized autoconvolution Volterra integral equations. Displaying a lower triangular matrix for basis functions, the corresponding solution is represented in matrix form, and an infinite upper triangular Toeplitz matrix is used to show the matrix representation of the integral part of the autoconvolution integral equation. …”
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Computational Methods for Solving Linear Fuzzy Volterra Integral Equation by Jihan Hamaydi, Naji Qatanani

“…Two numerical schemes, namely, the Taylor expansion and the variational iteration methods, have been implemented to give an approximate solution of the fuzzy linear Volterra integral equation of the second kind. To display the validity and applicability of the numerical methods, one illustrative example with known exact solution is presented. …”
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Analytical Solution of System of Volterra Integral Equations Using OHAM by Muhammad Akbar, Rashid Nawaz, Sumbal Ahsan, Dumitru Baleanu, Kottakkaran Sooppy Nisar

“…In this work, a reliable technique is used for the solution of a system of Volterra integral equations (VIEs), called optimal homotopy asymptotic method (OHAM). …”
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Singularly perturbed Volterra integral equations with weakly singular kernels by Angelina Bijura

“…We consider finding asymptotic solutions of the singularly perturbed linear Volterra integral equations with weakly singular kernels. An interesting aspect of these problems is that the discontinuity of the kernel causes layer solutions to decay algebraically rather than exponentially within the initial (boundary) layer. …”
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A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations by Wenxue Li, Meng Liu, Ke Wang

“…But it cannot be used for general stochastic Volterra integral equations (SVIEs). In this paper, we first introduce the concept of quasi-Itô process which is a generalization of well-known Itô process. …”
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Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method by Mohamed R. Ali, Mohamed M. Mousa, Wen-Xiu Ma

“…We present a new numerical technique to discover a new solution of Singular Nonlinear Volterra Integral Equations (SNVIE). The considered technique utilizes the Hybrid Orthonormal Bernstein and Block-Pulse functions wavelet method (HOBW) to solve the weakly SNVIE including Abel’s equations. …”
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Triangular Function Method is Adopted to Solve Nonlinear Stochastic It o^–Volterra Integral Equations by Guo Jiang, Dan Chen, Fugang Liu

“…This article presents the numerical solutions of nonlinear stochastic It o^–Volterra integral equations by using the basis function method under the global Lipschitz condition. …”
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Analytical Techniques for a Numerical Solution of the Linear Volterra Integral Equation of the Second Kind by M. I. Berenguer, D. Gámez, A. I. Garralda-Guillem, M. Ruiz Galán, M. C. Serrano Pérez

“…In this work we use analytical tools—Schauder bases and Geometric Series theorem—in order to develop a new method for the numerical resolution of the linear Volterra integral equation of the second kind.…”
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On a modified Bernstein operators approximation method for computational solution of Volterra integral equation by Khursheed J. Ansari, Fuat Usta

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A New Modification of Adomian Decomposition Method for Volterra Integral Equations of the Second Kind by Lie-jun Xie

“…We propose a new modification of the Adomian decomposition method for Volterra integral equations of the second kind. By the Taylor expansion of the components apart from the zeroth term of the Adomian series solution, this new technology overcomes the problems arising from the previous decomposition method. …”
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Corrigendum to “Convergence Analysis of Legendre Pseudospectral Scheme for Solving Nonlinear Systems of Volterra Integral Equations” by Emran Tohidi, O. R. Navid Samadi, S. Shateyi

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Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels by Haotao Cai

“…We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. …”
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A New Approach for Solving Nonlinear 3D-Volterra Fuzzy Integral Equations by Hamid Mottaghi Golshan, Kianoush Fathi Vajargah, Reza Ezzati

Subjects: “…fuzzy volterra integral equation…”
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