Numerical differentiation of implicitly defined curves

Syam, Muhammed I.; Siyyam, Hani I.

doi:10.1016/s0377-0427(99)00106-5

Cited by 21 publications

(8 citation statements)

References 3 publications

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“…In addition, artificial neural networks [20], the optimal homotopy asymptotic method [8] and the Laplace-Adomian-Pade method [12], Bäcklund transformation [17], and He's variational iteration method [9], are used to solved this problem. More methods can be found in [1,5,6,[22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Implicit hybrid methods for solving fractional Riccati equation

Syam¹,

Alsuwaidi²,

Alneyadi³

et al. 2018

J. Nonlinear Sci. Appl.

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In this paper, we modify the implicit hybrid methods for solving fractional Riccati equation. Similar methods are implemented for the ordinary derivative and we are the first who implement it for fractional derivative case. This approach is of higher order comparing with the existing methods in the literature. We study the convergence, zero stability, consistency, and region of absolute stability. Numerical results are presented to show the efficiency of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Implicit hybrid methods for solving fractional Riccati equation

Syam¹,

Alsuwaidi²,

Alneyadi³

et al. 2018

J. Nonlinear Sci. Appl.

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“…If (u i , k i ) lies sufficiently enough near the curve c, then the corrector process will converge for sufficiently small stepsize. For more details, see [1,[17][18][19][20]. We will classify the points into regular and singular points.…”

Section: Review Of Path-following Methodsmentioning

confidence: 99%

The modified Broyden-variational method for solving nonlinear elliptic differential equations

Syam

2007

Chaos, Solitons & Fractals

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“…The second condition is called the reproducing property and a Hilbert space which possesses a reproducing kernel is called a reproducing kernel Hilbert space (RKHS). More details can be in [7][8][9][10][11][12][13][14]. A description of the RKM for discretization of the linear fractional Fredholm integrodifferential equations problem (4)-(5) is presented in Section 2.…”

Section: Definition Letmentioning

confidence: 99%

Reproducing Kernel Method for Solving Nonlinear Fractional Fredholm Integrodifferential Equation

Kashkari

Syam

2018

Complexity

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This article is devoted to both theoretical and numerical studies of nonlinear fractional Fredholm integrodifferential equations. In this paper, we implement the reproducing kernel method (RKM) to approximate the solution of nonlinear fractional Fredholm integrodifferential equations. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the solution of the nonlinear fractional Fredholm integrodifferential equation. Uniformly convergence of the approximate solution produced by the RKM to the exact solution is proven.

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Numerical differentiation of implicitly defined curves

Cited by 21 publications

References 3 publications

Implicit hybrid methods for solving fractional Riccati equation

Implicit hybrid methods for solving fractional Riccati equation

The modified Broyden-variational method for solving nonlinear elliptic differential equations

Reproducing Kernel Method for Solving Nonlinear Fractional Fredholm Integrodifferential Equation

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