Numerical Solution of Volterra-Fredholm Integral Equations Using Hybrid Orthonormal Bernstein and Block-Pulse Functions

Ramadan, Mohamed A.; Ali, Mohamed R.

doi:10.9734/arjom/2017/34324

Cited by 7 publications

(11 citation statements)

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“…The block-pulse implementation matrix of the fractional integration has been given in [14] as follows:…”

Section: Definition 1 the Riemann-liouville Fractional Integral Opermentioning

confidence: 99%

“…Numerical strategies for the SNVIE are spline collocation methods [3], Newton-Cotes methods [4], extrapolation algorithm [5], and Hermite-collocation method [6]. The most popular methods for talking about the such equations are introduced, such as homotopy asymptotic method [7], Nyström interpolant method [8], Mesh method [9], Tau method [10], Laplace transform [11], orthonormal Bernstein, and block-pulse functions [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method

Ali

Mousa

2019

Advances in Mathematical Physics

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We present a new numerical technique to discover a new solution of Singular Nonlinear Volterra Integral Equations (SNVIE). The considered technique utilizes the Hybrid Orthonormal Bernstein and Block-Pulse functions wavelet method (HOBW) to solve the weakly SNVIE including Abel’s equations. We acquire the HOBW implementation matrix of the integration to derive the procedure of solving these kind integral equations. The explained technique is delineated with two numerical cases to demonstrate the benefit of the technique used by us. At last, the exchange uncovers the way that the strategy utilized here is basic in usage.

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“…The block-pulse implementation matrix of the fractional integration has been given in [14] as follows:…”

Section: Definition 1 the Riemann-liouville Fractional Integral Opermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method

Ali

Mousa

2019

Advances in Mathematical Physics

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“…A general study has been given in [10] to construct both correct and series solutions to Lane-Emden equations through ADM. In [11][12][13][14][15][16][17][18] introduced Bernstein, several methods for numerical solutions of VIDE form the unique Emden-Fowler initial value problems. In [19] approach developed to obtain analytical-numerical solutions to two separate Lane-Emden problems.…”

Section: Function Approximation By the Hobw Functionsmentioning

confidence: 99%

“…So, the truncate of y(x) is y(x) = C T HOBW(x) the acquired results have been compared with that of my seven order (ADM) [13] along with the required solutions and introduced in Table 1. The outcomes reveal that the results by HOBW, with using only a small number of bases, are very promising and superior to ADM and evaluated absolute errors (AE) by HOBW for y(x) will be decreased rapidly in comparison with ADM.…”

Section: Illustrative Numerical Examplesmentioning

confidence: 99%

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A new algorithm for solving the nonlinear Lane–Emden equations arising in astrophysics

Ali

2019

SN Appl. Sci.

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Hybrid orthonormal Bernstein and block-pulse function wavelet method for many phenomena in mathematical physics and astrophysics is considered. We use a fundamental administrator and convert Lane-Emden conditions into necessary conditions. The upsides of utilizing the proposed strategy are introduced. At that point, an effective error estimation for the proposed technique is additionally presented lastly a few examinations and their numerical arrangements are given; and looking at between the numerical outcomes acquired from alternate strategies, we demonstrate the high exactness and productivity of the proposed strategy. Our method is characterized then the singular equations are transformed to Volterra integro-differential equations. We modify this equations to an algebraic system of equations. The solution to this application is achieved by solving this system and the constructed solutions are on approximation form. The acquired results guarantee the method provides a truncate solution to the Lane-Emden equations.

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A numerical method based on hybrid orthonormal Bernstein and improved block‐pulse functions for solving Volterra–Fredholm integral equations

Ramadan

Osheba

Hadhoud

2022

Numerical Methods Partial

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This paper deals with the numerical solution of the integral equations of linear second kind Volterra–Fredholm. These integral equations are commonly used in engineering and mathematical physics to solve many of the problems. A hybrid of Bernstein and improved block‐pulse functions method is introduced and used where the key point is to transform linear second‐type Volterra–Fredholm integral equations into an algebraic equation structure that can be solved using classical methods. Numeric examples are given which demonstrate the related features of the process.

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Numerical Solution of Volterra-Fredholm Integral Equations Using Hybrid Orthonormal Bernstein and Block-Pulse Functions

Cited by 7 publications

References 0 publications

Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method

Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method

A new algorithm for solving the nonlinear Lane–Emden equations arising in astrophysics

A numerical method based on hybrid orthonormal Bernstein and improved block‐pulse functions for solving Volterra–Fredholm integral equations

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