Approximate Solution of Integral Equation Using Bernstein Polynomial Multiwavelets

Suman, Suraj; Singh, Koushlendra Kumar; Pandey, Rajesh K.

doi:10.1007/978-81-322-1768-8_43

Cited by 1 publication

(2 citation statements)

References 14 publications

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“…BPMW ψ n,m (x) = ψ(k, n, m, x) have four arguments: n = 0, 1, ..., 2 k − 1, k is assumed to be any positive integer, m is the order of Bernstein polynomials and x is the normalized time. BPMW [Suman, S. et al (2014)] are defined on the interval [0, 1) as follows:…”

Section: Bernstein Polynomial Multiwavelets(bpmw)mentioning

confidence: 99%

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Bernstein polynomial multiwavelets operational matrices method for the numerical solution of system of linear Stratonovich Volterra integral equations

Shiralashetti¹,

Lamani²

2021

JSR

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This article gives an effective strategy to solve the system of linear Stratonovich Volterra integral equations. Using the Bernstein polynomial multiwavelets operational matrix of integration and its stochastic operational matrix of integration, the system of linear Stratonovich Volterra integral equations can be reduced to a system of linear algebraic equations with unknown coefficients, and the obtained linear algebraic equations are solved numerically. Error analysis of the proposed method is given. Numerical examples are presented to show that the method described is accurate and precise. Keywords-Bernstein polynomials, Bernstein polynomial multiwavelets, Brownian motion, Stratonovich Volterra integral equations, Stochastic operational matrix of integration of Bernstein polynomial multiwavelets.

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Section: Bernstein Polynomial Multiwavelets(bpmw)mentioning

confidence: 99%

“…In equation 5, W B m is the orthonormal form of Berstein polynomials of order m. These orthonormal form of Berstein polynomials are obtained by using Gram-Schmidt orthonormalization process on Berstein polynomials [Suman, S. et al (2014)] B i,m (x). For instance, for M = 3, orthonormal polynomials are given by,…”

Section: Bernstein Polynomial Multiwavelets(bpmw)mentioning

confidence: 99%

Bernstein polynomial multiwavelets operational matrices method for the numerical solution of system of linear Stratonovich Volterra integral equations

Shiralashetti¹,

Lamani²

2021

JSR

View full text Add to dashboard Cite

show abstract

Approximate Solution of Integral Equation Using Bernstein Polynomial Multiwavelets

Cited by 1 publication

References 14 publications

Bernstein polynomial multiwavelets operational matrices method for the numerical solution of system of linear Stratonovich Volterra integral equations

Bernstein polynomial multiwavelets operational matrices method for the numerical solution of system of linear Stratonovich Volterra integral equations

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