Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions

Babolian, E.; Shamloo, Ali Salimi

doi:10.1016/j.cam.2007.03.007

Cited by 66 publications

(47 citation statements)

References 5 publications

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“…If we consider y T by the diagonal matrix, then we have d i y T = y T d i and for every α i , D αi has an operational matrix E αi then by substituting this into equation (6) we have If y(t) is approximated by y m (t) = m 1 y i β i (t) , we find y i (y i is approximation of y i and y = m 1 y i β i (t)), from [5] we have following error bound…”

Section: Numerical Methods and Error Estimationmentioning

confidence: 99%

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Numerical solution of fractional differential, integral and integro‐differential equations by using piecewise constant orthogonal functions

Shamloo

Babolian

2007

Proc Appl Math and Mech

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Section: Numerical Methods and Error Estimationmentioning

confidence: 99%

“…and Δ i = 0 for i ≥ m (see [3,5]). We can also show every piecewise constant orthogonal functions by a diagonal matrix.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of fractional differential, integral and integro‐differential equations by using piecewise constant orthogonal functions

Shamloo

Babolian

2007

Proc Appl Math and Mech

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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%

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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Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions

Cited by 66 publications

References 5 publications

Numerical solution of fractional differential, integral and integro‐differential equations by using piecewise constant orthogonal functions

Numerical solution of fractional differential, integral and integro‐differential equations by using piecewise constant orthogonal functions

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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