A new Bernoulli wavelet method for accurate solutions of nonlinear fuzzy Hammerstein–Volterra delay integral equations

2017 ◽  
Vol 309 ◽  
pp. 131-144 ◽  
Author(s):  
P.K. Sahu ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Wavelet Method ◽  
Bernoulli Wavelet

Application of Bernoulli wavelet method to solve a system of fuzzy integral equations

2018 ◽  
Vol 9 (1-2) ◽  
pp. 16-27 ◽  
Author(s):  
Mohamed Abdel- Latif Ramadan ◽  
Mohamed R. Ali
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Bernoulli Polynomials ◽  
Approximate Solutions ◽  
Fredholm Integral Equations ◽  
Fuzzy Integral ◽  
Algebraic Equations ◽  
Wavelet Method ◽  
Numerical Examples ◽  
Bernoulli Wavelet

In this paper, an efficient numerical method to solve a system of linear fuzzy Fredholm integral equations of the second kind based on Bernoulli wavelet method (BWM) is proposed. Bernoulli wavelets have been generated by dilation and translation of Bernoulli polynomials. The aim of this paper is to apply Bernoulli wavelet method to obtain approximate solutions of a system of linear Fredholm fuzzy integral equations. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, then we used it to transform the integral equations to the system of algebraic equations. The error estimates of the proposed method is given and compared by solving some numerical examples.

Numerical study of stochastic Volterra–Fredholm integral equations by using second kind Chebyshev wavelets

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Fakhrodin Mohammadi ◽  
Parastoo Adhami
Keyword(s):  
Integral Equations ◽  
Numerical Study ◽  
Operational Matrix ◽  
Computational Method ◽  
Fredholm Integral Equations ◽  
Wavelet Method ◽  
Chebyshev Wavelets ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix ◽  
Efficiency And Reliability

AbstractIn this paper, we present a computational method for solving stochastic Volterra–Fredholm integral equations which is based on the second kind Chebyshev wavelets and their stochastic operational matrix. Convergence and error analysis of the proposed method are investigated. Numerical results are compared with the block pulse functions method for some non-trivial examples. The obtained results reveal efficiency and reliability of the proposed wavelet method.

scholarly journals A Comparative Study on Haar Wavelet and Hosaya Polynomial for the numerical solution of Fredholm integral equations

2018 ◽  
Vol 3 (2) ◽  
pp. 447-458 ◽  
Author(s):  
S.C. Shiralashetti ◽  
H. S. Ramane ◽  
R.A. Mundewadi ◽  
R.B. Jummannaver
Keyword(s):  
Error Analysis ◽  
Comparative Study ◽  
Numerical Solution ◽  
Integral Equations ◽  
Haar Wavelet ◽  
Fredholm Integral Equations ◽  
Polynomial Method ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Hosoya Polynomial

AbstractIn this paper, a comparative study on Haar wavelet method (HWM) and Hosoya Polynomial method(HPM) for the numerical solution of Fredholm integral equations. Illustrative examples are tested through the error analysis for efficiency. Numerical results are shown in the tables and figures.

AN EFFICIENT NUMERICAL APPROACH FOR SOLVING ABEL’S INTEGRAL EQUATIONS BY USING MODIFIED TAYLOR WAVELETS

2021 ◽  
Vol 10 (5) ◽  
pp. 2285-2294
Author(s):  
A. Kumar ◽  
S. R. Verma
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Numerical Approach ◽  
Algebraic Equations ◽  
Wavelet Method

In this paper, a modified Taylor wavelet method (MTWM) is developed for numerical solutions of various types of Abel's integral equations. This method is based on the modified Taylor wavelet (MTW) approximation. The purpose behind using the MTW approximation is to transform the introduction problems into an equivalent set of algebraic equations. To check the accuracy and applicability of the proposed method, some examples have been solved and compared with other existing methods.

scholarly journals Solving Fuzzy Volterra Integrodifferential Equations of Fractional Order by Bernoulli Wavelet Method

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
R. Mastani Shabestari ◽  
R. Ezzati ◽  
T. Allahviranloo
Keyword(s):  
Integrodifferential Equation ◽  
Matrix Equation ◽  
Matrix Method ◽  
Integrodifferential Equations ◽  
Algebraic Equations ◽  
Wavelet Method ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Bernoulli Wavelet ◽  
Fractional Integrodifferential Equation

A matrix method called the Bernoulli wavelet method is presented for numerically solving the fuzzy fractional integrodifferential equations. Using the collocation points, this method transforms the fuzzy fractional integrodifferential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown coefficients. To illustrate the method, it is applied to certain fuzzy fractional integrodifferential equations, and the results are compared.

scholarly journals Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

2019 ◽  
Vol 4 (2) ◽  
pp. 395-406 ◽  
Author(s):  
R. A. Mundewadi ◽  
Kumbinarasaiah S
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Integral Equations ◽  
High Accuracy ◽  
Algebraic Equations ◽  
Wavelet Method

AbstractA numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

A New Bernoulli Wavelet Method for Numerical Solutions of Nonlinear Weakly Singular Volterra Integro-Differential Equations

2017 ◽  
Vol 14 (03) ◽  
pp. 1750022 ◽  
Author(s):  
P. K. Sahu ◽  
S. Saha Ray
Keyword(s):  
Differential Equations ◽  
Convergence Analysis ◽  
Present Method ◽  
Numerical Solutions ◽  
Bernoulli Polynomials ◽  
Algebraic Equations ◽  
Wavelet Method ◽  
Weakly Singular ◽  
Nonlinear Algebraic Equations ◽  
Bernoulli Wavelet

In this paper, Bernoulli wavelet method has been developed to solve nonlinear weakly singular Volterra integro-differential equations. Bernoulli wavelets are generated by dilation and translation of Bernoulli polynomials. The properties of Bernoulli wavelets and Bernoulli polynomials are first presented. The present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by Newton’s method. Convergence analysis of the present method has been discussed in this paper. Some illustrative examples have been demonstrated to show the applicability and accuracy of the present method.

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