Numerical solution of semidifferential equations by collocation method

Rawashdeh, Edris

doi:10.1016/j.amc.2005.05.029

Cited by 20 publications

(12 citation statements)

References 4 publications

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“…Thus, using the procedures of the RPS algorithm [25][26][27][28], the 4th RPS approximate solution of FBTEs (13) and (14) can be given by ω 4 (t) = 2t 4α Γ(4α+1) . Consequently, the RPS solution at α = 1/2 will be ω(t) = t 2 , which is fully compatible with the exact solution investigated earlier in [32].…”

Section: Numerical Experimentssupporting

confidence: 85%

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Residual Power Series Technique for Simulating Fractional Bagley–Torvik Problems Emerging in Applied Physics

et al. 2019

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Featured Application: Fractional differential equations play a significant role in modeling certain dynamical systems arising in many fields of applied sciences and engineering. In this paper, the authors develop an attractive analytic-numeric technique, residual power series (RPS) method, for solving fractional Bagley-Torvik equations with a source term involving Caputo fractional derivative. In regard to its simplicity, the method can be applicable to a wide class of fractional partial differential equations, fractional fuzzy differential equations, fractional oscillator equations, and so on.Abstract: Numerical simulation of physical issues is often performed by nonlinear modeling, which typically involves solving a set of concurrent fractional differential equations through effective approximate methods. In this paper, an analytic-numeric simulation technique, called residual power series (RPS), is proposed in obtaining the numerical solution a class of fractional Bagley-Torvik problems (FBTP) arising in a Newtonian fluid. This approach optimizes the solutions by minimizing the residual error functions that can be directly applied to generate fractional PS with a rapidly convergent rate. The RPS description is presented in detail to approximate the solution of FBTPs by highlighting all the steps necessary to implement the algorithm in addressing some test problems. The results indicate that the RPS algorithm is reliable and suitable in solving a wide range of fractional differential equations applying in physics and engineering.

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Section: Numerical Experimentssupporting

confidence: 85%

“…This model is a special case of FBTE that arises in the modelling of the motion of a rigid plate immersed in a Newtonian fluid [32]. To apply the proposed algorithm, we have to solve the equivalent system by letting…”

Section: Numerical Experimentsmentioning

confidence: 99%

Residual Power Series Technique for Simulating Fractional Bagley–Torvik Problems Emerging in Applied Physics

et al. 2019

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“…Rawashdeh used the collocation spline method to approximate the solution of semidifferential equation, which was a special kind of fractional integro differential equations. Rawashdeh proposed collocation method for the numerical solution of fractional IPDEs.…”

Section: Introductionmentioning

confidence: 99%

B‐spline solution of fractional integro partial differential equation with a weakly singular kernel

Arshed

2017

Numerical Methods Partial

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The main objective of the paper is to find the approximate solution of fractional integro partial differential equation with a weakly singular kernel. Integro partial differential equation (IPDE) appears in the study of viscoelastic phenomena. Cubic B‐spline collocation method is employed for fractional IPDE. The developed scheme for finding the solution of the considered problem is based on finite difference method and collocation method. Caputo fractional derivative is used for time fractional derivative of order α, 0 < α < 1 . The given problem is discretized in both time and space directions. Backward Euler formula is used for temporal discretization. Collocation method is used for spatial discretization. The developed scheme is proved to be stable and convergent with respect to time. Approximate solutions are examined to check the precision and effectiveness of the presented method.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1565–1581, 2017

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“…Additionally, algorithm based on quadrature formula is introduced in [12], as well as in [13], along with the implementation of the so-called fractional multistep methods discussed in [21,22]. The use of spline approximation [9] and collocation method [34] has been effectively implemented for the solution of initial value fractional differential equations. Additionally, the cubic spline collocation method to solve two classes of special fractional boundary value problems involve the fractional derivative D 1=2 has been used in [17].…”

Section: Introductionmentioning

confidence: 99%