Numerical Solutions of Fractional Differential Equations by Using Laplace Transformation Method and Quadrature Rule [PDF]
Fractal and Fractional, 2021 This paper introduces an efficient numerical scheme for solving a significant class of fractional differential equations. The major contributions made in this paper apply a direct approach based on a combination of time discretization and the Laplace ...
Samaneh Soradi-Zeid +2 more
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A Time Finite Element Method Based on the Differential Quadrature Rule and Hamilton’s Variational Principle [PDF]
Applied Sciences, 2017 An accurate and efficient Differential Quadrature Time Finite Element Method (DQTFEM) was proposed in this paper to solve structural dynamic ordinary differential equations.
Yufeng Xing, Mingbo Qin, Jing Guo
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Legendre wavelet method combined with the Gauss quadrature rule for numerical solution of fractional integro-differential equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 In this paper, we use a novel technique to solve the nonlinear fractional Volterra-Fredholm integro-differential equations (FVFIDEs). To this end, the Legendre wavelets are used in conjunction with the quadrature rule for converting the problem into a ...
M. Riahi Beni
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An Improved Differential Quadrature Time Element Method
Applied Sciences, 2017 A Differential Quadrature Time Element Method (DQTEM) was proposed by the author and co-worker, its drawback is the need of larger storage capacity since the dimension of the coefficients matrix for solution is the product of both spatial degrees of ...
Mingbo Qin, Yufeng Xing, Jing Guo
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Stress-driven Approach to Vibrational Analysis of FGM Annular Nano-plate based on First-order Shear Deformation Plate Theory [PDF]
Journal of Applied and Computational Mechanics, 2023 Vibrational behavior of small-scale functionally graded annular plate based on the first-order shear deformation theory, and non-local stress-driven model is investigated.
Mojtaba Shariati +2 more
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Effective numerical methods for nonlinear singular two-point boundary value Fredholm integro-differential equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2023 We deal with some effective numerical methods for solving a class of nonlinear singular two-point boundary value Fredholm integro-differential equations.
S. Amiri
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On quadrature rules for solving Partial Differential Equations using Neural Networks
Computer Methods in Applied Mechanics and Engineering, 2022 Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may arise in these applications and propose different alternatives to overcome them, namely: Monte Carlo methods ...
Rivera, Jon A. +3 more
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Exponential Quadrature Rules for Linear Fractional Differential Equations [PDF]
Mediterranean Journal of Mathematics, 2014 This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized Mittag-Leffler function. Then suitable quadrature rules are devised and order conditions of algebraic type are derived.
Garrappa R., POPOLIZIO, MARINA
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Journal of Mathematics, 2023 Laplace transform has been used for solving differential equations of fractional order either PDEs or ODEs. However, using the Laplace transform sometimes leads to solutions in Laplace space that are not readily invertible to the real domain by ...
null Kamran +4 more
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Quadrature Integration Techniques for Random Hyperbolic PDE Problems
Mathematics, 2021 In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also
Rafael Company +2 more
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