scholarly journals Numerical Solution of Nonlinear Fredholm Integrodifferential Equations by Hybrid of Block-Pulse Functions and Normalized Bernstein Polynomials

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
S. H. Behiry
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Present Method ◽  
Bernstein Polynomials ◽  
Integrodifferential Equations ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Nonlinear Algebraic Equations

A numerical method for solving nonlinear Fredholm integrodifferential equations is proposed. The method is based on hybrid functions approximate. The properties of hybrid of block pulse functions and orthonormal Bernstein polynomials are presented and utilized to reduce the problem to the solution of nonlinear algebraic equations. Numerical examples are introduced to illustrate the effectiveness and simplicity of the present method.

scholarly journals A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Changqing Yang ◽  
Jianhua Hou
Keyword(s):  
Differential Equation ◽  
Numerical Method ◽  
Collocation Method ◽  
Chebyshev Polynomials ◽  
Initial Value Problems ◽  
Algebraic Equations ◽  
Initial Value ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions

A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

scholarly journals Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid Functions and the Collocation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Jianhua Hou ◽  
Beibo Qin ◽  
Changqing Yang
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Taylor Series ◽  
Fredholm Integral Equations ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Hybrid Function ◽  
Nonlinear Fredholm Integral Equations

A numerical method to solve nonlinear Fredholm integral equations of second kind is presented in this work. The method is based upon hybrid function approximate. The properties of hybrid of block-pulse functions and Taylor series are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of algebraic equations. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

scholarly journals Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. Mashayekhi ◽  
M. Razzaghi ◽  
O. Tripak
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Bernoulli Polynomials ◽  
Fredholm Integral Equations ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Block Pulse Functions

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

scholarly journals Numerical Solution of Time-Fractional Order Telegraph Equation by Bernstein Polynomials Operational Matrices

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
M. Asgari ◽  
R. Ezzati ◽  
T. Allahviranloo
Keyword(s):  
Linear System ◽  
Numerical Solution ◽  
Fractional Order ◽  
Original Problem ◽  
Bernstein Polynomials ◽  
Telegraph Equation ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Fractional Differential

We present a new method to solve time-fractional order telegraph equation (TFOTE) by using Bernstein polynomials. By implementation of Bernstein polynomials operational matrices of fractional differential on TFOTE, we reduce the original problem to a linear system of algebraic equations. Also, we prove the convergence analysis. In order to show the efficiency of the proposed method, we present two numerical examples.

scholarly journals A Hybrid Function Approach to Solving a Class of Fredholm and Volterra Integro-Differential Equations

2020 ◽  
Vol 25 (2) ◽  
pp. 30
Author(s):  
Aline Hosry ◽  
Roger Nakad ◽  
Sachin Bhalekar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Numerical Method ◽  
Approximate Solutions ◽  
Function Approach ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Block Pulse Functions ◽  
Hybrid Function ◽  
Derivatives Of

In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The key point is to derive a new approximation for the derivatives of the solutions and then reduce the integro-differential equation to a system of algebraic equations that can be solved using classical methods. Some numerical examples are dedicated for showing the efficiency and validity of the method that we introduce.

scholarly journals On Bernstein Polynomials Method to the System of Abel Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Jafarian ◽  
S. Measoomy Nia ◽  
Alireza K. Golmankhaneh ◽  
D. Baleanu
Keyword(s):  
Linear System ◽  
Numerical Solution ◽  
Integral Equations ◽  
Bernstein Polynomials ◽  
Singular System ◽  
Special Kind ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Abel Integral Equations ◽  
The Given

This paper deals with a new implementation of the Bernstein polynomials method to the numerical solution of a special kind of singular system. For this aim, first the truncated Bernstein series polynomials of the solution functions are substituted in the given problem. Using some properties of these polynomials, the solution of the problem is reduced to solve a linear system of algebraic equations. In order to confirm the reliability and accuracy of the proposed method, some weakly Abel integral equations systems with comparisons are solved in detail as numerical examples.

Bernstein polynomials for solving fractional heat- and wave-like equations

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
Davood Rostamy ◽  
Kobra Karimi
Keyword(s):  
Numerical Analysis ◽  
Numerical Solution ◽  
Fractional Derivatives ◽  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Fractional Differential

AbstractIn this paper, a novel numerical analysis is introduced and performed to obtain the numerical solution of the fractional heat- and wave-like equations. A general formulation for the Bernstein fractional derivatives operational matrix is given. In this approach, a truncated Bernstein series together with the Bernstein operational matrix of fractional derivatives are used to reduce the solution of fractional differential problems to the solution of a system of algebraic equations. Numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results.

scholarly journals Numerical solution of two dimensional nonlinear fuzzy Fredholm integral equations of second kind using hybrid of block-pulse functions and Bernstein polynomials

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4923-4935 ◽  
Author(s):  
Vahid Mahaleh ◽  
Reza Ezzati
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Approximation Method ◽  
Numerical Stability ◽  
Bernstein Polynomials ◽  
Fredholm Integral Equations ◽  
Successive Approximation Method ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Block Pulse Functions

In this paper, first, we introduce a successive approximation method in terms of a combination of Bernstein polynomials and block-pulse functions. The proposed method is given for solving two dimensional nonlinear fuzzy Fredholm integral equations of the second kind. Then, we present the convergence of the proposed method. Also we investigate the numerical stability of the method with respect to the choice of the first iteration. Finally, two numerical examples are presented to show the accuracy of the method.

scholarly journals Solution of Nonlinear Volterra-Fredholm Integrodifferential Equations via Hybrid of Block-Pulse Functions and Lagrange Interpolating Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hamid Reza Marzban ◽  
Sayyed Mohammad Hoseini
Keyword(s):  
Differential Equations ◽  
Hybrid Method ◽  
High Order ◽  
Integrodifferential Equations ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Interpolating Polynomials ◽  
Lagrange Interpolating Polynomials

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations to the solution of algebraic equations whose solution is much more easier than the original one. The validity and applicability of the proposed method are demonstrated through illustrative examples. The method is simple, easy to implement and yields very accurate results.

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