Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

Pourdarvish, A.; Sayevand, Khosro; Masti, I.; Kumar, Sunil

doi:10.1007/s40819-022-01246-z

Int. J. Appl. Comput. Math

2022

DOI: 10.1007/s40819-022-01246-z

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Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

A. Pourdarvish

Khosro Sayevand

I. Masti

et al.

Abstract: Analyzing the mathematical models involving Itô integral, in particular in science and engineering has received much attention, and the reason for this issue is the randomness and lack of access to the exact answer of this type of models. For this purpose, in this paper, the approximate solution of two dimensional (2-D) stochastic Volterra–Fredholm integral equations (SVFIEs) based on the operational matrix method and orthonormal Bernoulli polynomials (OBP) is investigated. Some results and convergence analysi… Show more

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Cited by 2 publications

References 22 publications

(33 reference statements)

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Residual power series scheme treatments for fractional Klein-Gordon problem arising in soliton theory

Rida,

Arafa,

Hussein

et al. 2024

Sci Rep

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The Klein-Gordon problem (KGP) is one of the interesting models that appear in many scientific phenomena. These models are characterized by memory effects, which provide insight into complex phenomena in the fields of physics. In this regard, we propose a new robust algorithm called the confluent Bernoulli approach with residual power series scheme (CBCA-RPSS) to give an approximate solution for the fractional nonlinear KGP. The convergence, uniqueness and error analysis of the proposed method are discussed in detail. A comparison of the numerical results obtained by CBCA-RPSS with the results obtained by some well-known algorithms is presented. Numerical simulations using base errors indicate that CBCA-RPSS is an accurate and efficient technique and thus can be used to solve linear and nonlinear fractional models in physics and engineering. All the numerical results for the studied problems were obtained through implementation codes in Matlab R2017b.

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Residual power series scheme treatments for fractional Klein-Gordon problem arising in soliton theory

Rida,

Arafa,

Hussein

et al. 2024

Sci Rep

View full text Add to dashboard Cite

show abstract

On analyzing two dimensional fractional order brain tumor model based on orthonormal Bernoulli polynomials and Newton's method

Masti,

Khosro Sayevand,

Jafari

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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Recently, modeling problems in various field of sciences and engineering with the help of fractional calculus has been welcomed by researchers. One of these interesting models is a brain tumor model. In this framework, a two dimensional expansion of the diffusion equation and glioma growth is considered. The analytical solution of this model is not an easy task, so in this study, a numerical approach based on the operational matrix of conventional orthonormal Bernoulli polynomials (OBPs) has been used to estimate the solution of this model. As an important advantage of the proposed method is to obtain the fractional derivative in matrix form, which makes calculations easier. Also, by using this technique, the problem under the study is converted into a system of nonlinear algebraic equations. This system is solved via Newton's method and the error analysis is presented. At the end to show the accuracy of the work, we have examined two examples and compared the numerical results with other works.

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Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

Cited by 2 publications

References 22 publications

Residual power series scheme treatments for fractional Klein-Gordon problem arising in soliton theory

Residual power series scheme treatments for fractional Klein-Gordon problem arising in soliton theory

On analyzing two dimensional fractional order brain tumor model based on orthonormal Bernoulli polynomials and Newton's method

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