Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions

Babolian, E.; Masouri, Zahra

doi:10.1016/j.cam.2007.07.029

Cited by 83 publications

(52 citation statements)

References 7 publications

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“…However, our method is different from the methods, as presented in [32] and [33]. Consider Example 1, in Table 6, the expansion-iterative method and direct method are compared with our method.…”

Section: Comparisonmentioning

confidence: 98%

Bernstein Multiscaling polynomials and application by solving Volterra integral equations

2016

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In this paper, we present a direct computational method to solve Volterra integral equations. The proposed method is a direct method based on approximate functions with the Bernstein Multiscaling polynomials. In this method, using operational matrices, the integral equation turns into a system of equations. Our approach can solve nonlinear integral equations of the first kind and the second kind with piecewise solution. The computed operational matrices in this article are exact and new. The comparison of obtained solutions with the exact solutions shows that this method is acceptable. We also compared our approach with two direct and expansion-iterative methods based on the block-pulse functions. Our method produces a system, which is more economical, and the solutions are more accurate. Moreover, the stability of the proposed method is studied and analyzed by examining the noise effect on the data function. The appropriateness of noisy solutions with the amount of noise approves that the method is stable.

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Section: Comparisonmentioning

confidence: 98%

Bernstein Multiscaling polynomials and application by solving Volterra integral equations

2016

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“…Block-pulse functions (BPFs) have been studied by many authors and applied for solving different problems; for example, see [44,45].…”

Section: Block-pulse Functionsmentioning

confidence: 99%

“…The third property is completeness. For every f ∈ L 2 ([0, 1)) when m approaches to the infinity, Parseval's identity holds [44]:…”

Section: Definitionmentioning

confidence: 99%

A Moment Method Simulation of Electromagnetic Scattering From Conducting Bodies

Hatamzadeh-Varmazyar¹,

Naser‐Moghadasi²,

Masouri³

2008

PIER

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Abstract-In this paper a moment method simulation of electromagnetic scattering problem is presented. An effective numerical method for solving this problem based on the method of moments and using block-pulse basis functions is proposed. Some examples of engineering interest are included to illustrate the procedure. The scattering problem is treated in detail, and illustrative computations are given for some cases. This method can be generalized to apply to objects of arbitrary geometry and arbitrary material.

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“…Block-pulse functions are studied by many authors and applied for solving different problems; for example, see [30,31].…”

Section: Review Of Block-pulse Functionsmentioning

confidence: 99%

New Direct Method to Solve Nonlinear Volterra-Fredholm Integral and Integro-Differential Equations Using Operational Matrix With Block-Pulse Functions

Babolian¹,

Masouri²,

Hatamzadeh-Varmazyar³

2008

PIER B

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Abstract-A new and effective direct method to determine the numerical solution of specific nonlinear Volterra-Fredholm integral and integro-differential equations is proposed. The method is based on vector forms of block-pulse functions (BPFs). By using BPFs and its operational matrix of integration, an integral or integro-differential equation can be transformed to a nonlinear system of algebraic equations.Some numerical examples are provided to illustrate accuracy and computational efficiency of the method. Finally, the error evaluation of this method is presented. The benefits of this method are low cost of setting up the equations without applying any projection method such as Galerkin, collocation, . . . . Also, the nonlinear system of algebraic equations is sparse.

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Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions

Cited by 83 publications

References 7 publications

Bernstein Multiscaling polynomials and application by solving Volterra integral equations

Bernstein Multiscaling polynomials and application by solving Volterra integral equations

A Moment Method Simulation of Electromagnetic Scattering From Conducting Bodies

New Direct Method to Solve Nonlinear Volterra-Fredholm Integral and Integro-Differential Equations Using Operational Matrix With Block-Pulse Functions

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