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Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 07/2018, Volume 41, Issue 10, pp. 3841 - 3855
In this paper, we construct a new fractional weighted reproducing kernel space, which is the minimum space containing the exact solution. The closed form of... 
weakly singular kernel | fractional reproducing kernel space | fractional integro‐differential equation | fractional integro-differential equation | ORDER | MATHEMATICS, APPLIED | COLLOCATION METHOD | Differential equations | Error correction | Mathematical analysis | Exact solutions
Journal Article
Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 09/2017, Volume 33, Issue 5, pp. 1565 - 1581
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 08/2019, Volume 354, pp. 103 - 114
In this paper, we propose a fast and efficient numerical method to solve the two-dimensional integro-differential equation with a weakly singular kernel. The... 
Integro-differential equation with weakly singular kernel | Stability | Convolution quadrature rule | ADI difference scheme | Convergence | ORDER | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | CONVOLUTION QUADRATURE | APPROXIMATIONS | EVOLUTION EQUATION | TIME DISCRETIZATION | Analysis | Differential equations
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 07/2018, Volume 328, pp. 353 - 364
In this paper, we consider the hybrid collocation methods to solve the eigenvalue problem of a compact integral operator with weakly singular kernels of... 
Hybrid collocation methods | Eigenvalue problem | Convergence rates | Weakly singular kernel | MATHEMATICS, APPLIED | APPROXIMATION | EQUATIONS | 2ND KIND | PRODUCT INTEGRATION
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 02/2013, Volume 234, Issue 1, pp. 317 - 329
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 02/2016, Volume 275, pp. 72 - 80
In this paper, based on the second Chebyshev wavelets (SCW) operational matrix of fractional order integration, a numerical method for solving a class of... 
Operational matrix | Weakly singular integro-differential equations | Block pulse functions | SCW | Fractional calculus | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | INTEGRATION | CALCULUS | MATRICES | Methods | Differential equations
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2019, Volume 346, pp. 224 - 236
In this paper, we consider Legendre multi-Galerkin methods to solve Fredholm integral equations of the second kind with weakly singular kernel and the... 
Eigenvalue problem | Legendre spectral methods | Multi-Galerkin methods | Fredholm integral equations | Weakly singular kernel | MATHEMATICS, APPLIED | APPROXIMATION | PROJECTION METHODS | PRODUCT INTEGRATION
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 7627 - 7639
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 08/2016, Volume 302, pp. 71 - 80
Two reliable methods, namely the Adomian decomposition method (ADM) and the variational iteration method (VIM), are used for solving the Volterra integral... 
Variational iteration method | Adomian decomposition method | Weakly singular Volterra equation | TRANSFORMATION | MATHEMATICS, APPLIED | ALGORITHM | Kernels | Sequences | Approximation | Mathematical analysis | Mathematical models | Decomposition | Iterative methods | Volterra integral equations
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2019, Volume 42, Issue 13, pp. 4427 - 4443
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 08/2015, Volume 39, Issue 15, pp. 4421 - 4431
The Jacobi spectral Galerkin method for Volterra integral equations of the second kind with a weakly singular kernel is proposed in this paper. We provide a... 
Volterra integral equation | Jacobi spectral Galerkin method | Weakly singular kernel | Convergence | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | POLYNOMIAL-APPROXIMATION | ENGINEERING, MULTIDISCIPLINARY
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 06/2015, Volume 260, pp. 63 - 70
Numerical methods for weakly singular Volterra integral equations are rarely considered in the literature. The solutions of such equations may exhibit a... 
Operational matrix | Weakly singular Volterra integral equations | Block pulse functions | SCW | Fractional calculus | Weakly singular | Volterra integral equations | KIND CHEBYSHEV WAVELET | MATHEMATICS, APPLIED | CALCULUS | INTEGRODIFFERENTIAL EQUATIONS | COLLOCATION METHODS
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 11/2016, Volume 69, Issue 2, pp. 673 - 695
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 01/2015, Volume 39, Issue 2, pp. 947 - 954
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2015, Volume 278, pp. 1 - 11
In this paper, the efficient methods are proposed for solving nonlinear Fredholm integral equations with a weakly singular kernel. By using Sinc approximation... 
Nonlinear Fredholm integral equation | Sinc approximation | Collocation method | Weakly singular kernel | Convergence analysis | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | APPROXIMATION | 2ND KIND
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 04/2019, Volume 347, pp. 149 - 161
This paper proposes a quadrature method based on multi-variate Bernstein polynomials. The method is used to solve multidimensional Volterra integral equations... 
Quadrature method | Error analysis | Weakly singular integral equation | Multi-variate Bernstein polynomial | MESHLESS METHOD | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | PARTIAL INTEGRODIFFERENTIAL EQUATION | SOLVE | RADIAL BASIS FUNCTIONS | 2ND KIND | COLLOCATION METHODS
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 13
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2017, Volume 323, pp. 136 - 146
Journal Article
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