A new numerical scheme for solving system of Volterra integro-differential equation

Loh, Jian Rong; Phang, Chang

doi:10.1016/j.aej.2017.01.021

Cited by 32 publications

(22 citation statements)

References 10 publications

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“…. , r ij } is continuously differentiable function up to the highest order of derivative contained in (32). We apply the idea of FIM-SCP described in Section 2 to deal with the integration term in (32).…”

Section: Numerical Solution For System Of Cidesmentioning

confidence: 99%

Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials

Duangpan

Boonklurb

Juytai³

2021

Fractal Fract

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In this paper, the finite integration method and the operational matrix of fractional integration are implemented based on the shifted Chebyshev polynomial. They are utilized to devise two numerical procedures for solving the systems of fractional and classical integro-differential equations. The fractional derivatives are described in the Caputo sense. The devised procedure can be successfully applied to solve the stiff system of ODEs. To demonstrate the efficiency, accuracy and numerical convergence order of these procedures, several experimental examples are given. As a consequence, the numerical computations illustrate that our presented procedures achieve significant improvement in terms of accuracy with less computational cost.

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Section: Numerical Solution For System Of Cidesmentioning

confidence: 99%

Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials

Duangpan

Boonklurb

Juytai³

2021

Fractal Fract

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“…(5). Then, the coefficients f mn can be calculated as follows (Dehestani et al 2020b;Loh and Phang 2018):…”

Section: Function Approximationmentioning

confidence: 99%

The novel operational matrices based on 2D-Genocchi polynomials: solving a general class of variable-order fractional partial integro-differential equations

2020

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The main purpose of this study was to introduce an efficient approximate approach for solving a general class of variable-order fractional partial integro-differential equations (VO-FPIDEs). First, the Genocchi polynomials properties and the pseudo-operational matrix of the VO-fractional derivative and fractional integration are presented. Then, to approximate an integral part of the problems, we obtain the dual pseudo-operational matrix of fractional order with a new technique. The pseudo-operational matrices of fractional order and Genocchi collocation method are applied to reduce the VO-FPIDEs to a system of algebraic equations. The error estimation indicates that the approximate solution converges to the exact solution. Also, we discuss in detail on the upper bound of error for the pseudo-operational matrix of fractional integration. In addition, to illustrate the efficiency and applicability of the approach, we present several numerical examples. Keywords Genocchi polynomials • Fractional pseudo-operational matrix • Variable-order fractional partial integro-differential equations • Mixed Riemann-Liouville integral • Variable-order fractional derivative Mathematics Subject Classification 26A33 • 33F05 • 35R09 Communicated by Agnieszka Malinowska.

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“…The exact solutions of these systems are difficult to find. In finding the approximate solutions, different approaches in the literature have been used such as homotopy perturbation method (HPM), 1 homotopy analysis method (HAM), 2 differential transformation method (DTM), 3 Genocchi polynomials (GP), 4 reproducing kernel Hilbert space method (RKHSM), 5 Chebyshev wavelets method (CWM), 6 fixed point method (FPM), 7 Sinc-collocation method (SCM), 8 Haar functions method (HFM), 9 Adomian decomposition method (ADM), 10 and relaxed Monte Carlo method (RMCM). 11 In the present attempt, optimal homotopy asymptotic method (OHAM) is used, which was introduced by Marinca et al 12,13 for the solution of differential equations.…”

Section: Introductionmentioning

confidence: 99%

Solutions of system of Volterra integro‐differential equations using optimal homotopy asymptotic method

Agarwal

Akbar

Nawaz

et al. 2020

Math Methods in App Sciences

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In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in the literature, and the obtained results are compared with Sinc‐collocation method. These results show the reliability and effectiveness of the proposed method. The proposed method does not require discretization like other numerical methods. Moreover, the convergence region can easily be controlled. The use of OHAM is simple and straightforward.

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A new numerical scheme for solving system of Volterra integro-differential equation

Cited by 32 publications

References 10 publications

Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials

Numerical Solutions for Systems of Fractional and Classical Integro-Differential Equations via Finite Integration Method Based on Shifted Chebyshev Polynomials

The novel operational matrices based on 2D-Genocchi polynomials: solving a general class of variable-order fractional partial integro-differential equations

Solutions of system of Volterra integro‐differential equations using optimal homotopy asymptotic method

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