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.

scholarly journals A numerical scheme for problems in fractional calculus

2018 ◽  
Vol 20 ◽  
pp. 02001
Author(s):  
M. Razzaghi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Numerical Scheme ◽  
Boundary Value ◽  
Bernoulli Polynomials ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Fractional Differential

In this paper, a new numerical method for solving the fractional differential equations with boundary value problems is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is given. This operator is then utilized to reduce the solution of the boundary value problems for fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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.

Analysis of Time-delay Systems via Hybrid of Block-pulse Functions and Taylor Series

2005 ◽  
Vol 11 (12) ◽  
pp. 1455-1468 ◽  
Author(s):  
H. R. Marzban ◽  
M. Razzaghi
Keyword(s):  
Time Delay ◽  
Taylor Series ◽  
Delay Systems ◽  
Operational Matrices ◽  
Time Delay Systems ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Hybrid Function

In this paper we present a method for finding the solution of time-delay systems using a hybrid function. We present the properties of the hybrid functions, which consist of block-pulse functions plus Taylor series. The method is based upon expanding various time functions in the system as their truncated hybrid functions. Operational matrices of integration and delay are presented and are utilized to reduce the solution of time-delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Solving systems of high-order linear ordinary differential equations with variable coefficients by means of exponential Chebyshev collocation method

2017 ◽  
Vol 8 (1-2) ◽  
pp. 40 ◽  
Author(s):  
Mohamed Ramadan ◽  
Kamal Raslan ◽  
Talaat El Danaf ◽  
Mohamed A. Abd Elsalam
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Variable Coefficients ◽  
High Order ◽  
Matrix Equations ◽  
Algebraic Equations ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Linear Algebraic Equations

The purpose of this paper is to investigate the use of exponential Chebyshev (EC) collocation method for solving systems of high-order linear ordinary differential equations with variable coefficients with new scheme, using the EC collocation method in unbounded domains. The EC functions approach deals directly with infinite boundaries without singularities. The method transforms the system of differential equations and the given conditions to block matrix equations with unknown EC coefficients. By means of the obtained matrix equations, a new system of equations which corresponds to the system of linear algebraic equations is gained. Numerical examples are given to illustrative the validity and applicability of the method.

scholarly journals Hybrid approximations for fractional calculus

2019 ◽  
Vol 29 ◽  
pp. 01001
Author(s):  
Mohsen Razzaghi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Initial Value Problems ◽  
Fractional Integral ◽  
Algebraic Equations ◽  
Initial Value ◽  
Hybrid Functions ◽  
Fractional Differential ◽  
Taylor Polynomials ◽  
Hybrid Approximations

In this paper, a numerical method for solving the fractional differential equations is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting ofblock-pulse functions and Taylor polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is given. This operator is then utilized to reduce the solution of the initial value problems for fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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.

Sign in / Sign up

Export Citation Format

Share Document