scholarly journals Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets

2005 ◽  
Vol 2005 (1) ◽  
pp. 113-121 ◽  
Author(s):  
M. Lakestani ◽  
M. Razzaghi ◽  
M. Dehghan
Keyword(s):  
Integral Equations ◽  
Algebraic Equations ◽  
B Spline ◽  
Compactly Supported ◽  
Hammerstein Integral Equations ◽  
Spline Wavelets

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated through an illustrative example.

SEMI-ORTHOGONAL SPLINE SCALING FUNCTIONS FOR SOLVING HAMMERSTEIN INTEGRAL EQUATIONS

2011 ◽  
Vol 09 (03) ◽  
pp. 427-443
Author(s):  
J. RASHIDINIA ◽  
ALI PARSA
Keyword(s):  
Integral Equations ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Absolute Error ◽  
Scaling Functions ◽  
Algebraic Equations ◽  
Maximum Absolute Error ◽  
Nonlinear Integral Equations ◽  
B Spline ◽  
Hammerstein Integral Equations

We developed a new numerical procedure based on the quadratic semi-orthogonal B-spline scaling functions for solving a class of nonlinear integral equations of the Hammerstein-type. Properties of the B-spline wavelet method are utilized to reduce the Hammerstein equations to some algebraic equations. The advantage of our method is that the dimension of the arising algebraic equation is 10 × 10. The operational matrix of semi-orthogonal B-spline scaling functions is sparse which is easily applicable. Error estimation of the presented method is analyzed and proved. To demonstrate the validity and applicability of the technique the method applied to some illustrative examples and the maximum absolute error in the solutions are compared with the results in existing methods.20,25,27,29

scholarly journals Maximum Vanishing Moment of Compactly Supported B-spline Wavelets

2019 ◽  
pp. 1-8
Author(s):  
Kanchan Lata Gupta ◽  
B. Kunwar ◽  
V. K. Singh
Keyword(s):  
Scaling Function ◽  
Simple Procedure ◽  
Smoothness Property ◽  
Vanishing Moments ◽  
B Spline ◽  
B Splines ◽  
Compactly Supported ◽  
Spline Wavelets ◽  
Vanishing Moment ◽  
Rule Order

Spline function is of very great interest in field of wavelets due to its compactness and smoothness property. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. We have given a simple procedure to generate compactly supported orthogonal scaling function for higher order B-splines in our previous work. Here we determine the maximum vanishing moments of the formed spline wavelet as established by the new refinable function using sum rule order method.

scholarly journals Convergence of approximate solution of mixed Hammerstein type integral equations

2018 ◽  
Vol 38 (2) ◽  
pp. 61-74
Author(s):  
Monireh Nosrati Sahlan
Keyword(s):  
Galerkin Method ◽  
Integral Equations ◽  
Basis Functions ◽  
Computational Method ◽  
Operational Matrices ◽  
B Spline ◽  
Spline Wavelets ◽  
Type Integral ◽  
The Galerkin Method ◽  
Dual Functions

In the present paper, a computational method for solving nonlinear Volterra-Fredholm Hammerestein integral equations is proposed by using compactly supported semiorthogonal cubic B-spline wavelets as basis functions. Dual functions and Operational matrices of B-spline wavelets via Galerkin method are utilized to reduce the computation of integral equations to some algebraic system, where in the Galerkin method dual of B-spline wavelets are applied as weighting functions. The method is computationally attractive, and applications are demonstrated through illustrative examples.

scholarly journals Solution of nonlinear Volterra-Hammerstein integral equations via single-term Walsh series method

2005 ◽  
Vol 2005 (5) ◽  
pp. 547-554 ◽  
Author(s):  
B. Sepehrian ◽  
M. Razzaghi
Keyword(s):  
Integral Equations ◽  
Walsh Series ◽  
Series Method ◽  
Algebraic Equations ◽  
Hammerstein Integral Equations ◽  
Single Term

Single-term Walsh series are developed to approximate the solutions of nonlinear Volterra-Hammerstein integral equations. Properties of single-term Walsh series are presented and are utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples.

scholarly journals Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
M. Lakestani ◽  
M. Razzaghi ◽  
M. Dehghan
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Scaling Functions ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Compactly Supported ◽  
Spline Wavelets

A method for solving the nonlinear second-order Fredholm integro-differential equations is presented. The approach is based on a compactly supported linear semiorthogonalB-spline wavelets. The operational matrices of derivative forB-spline scaling functions and wavelets are presented and utilized to reduce the solution of Fredholm integro-differential to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

scholarly journals Hermite collocation method for solving Hammerstein integral equations

2018 ◽  
Vol 14 (1) ◽  
pp. 7413-7423 ◽  
Author(s):  
Yasser Amer
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Matrix Equation ◽  
Unknown Function ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Hammerstein Integral Equations ◽  
The Matrix

In this paper, we are presenting Hermite collocation method to solve numer- ically the Fredholm-Volterra-Hammerstein integral equations. We have clearly presented a theory to …nd ordinary derivatives. This method is based on replace- ment of the unknown function by truncated series of well known Hermite expan-sion of functions. The proposed method converts the equation to matrix equation which corresponding to system of algebraic equations with Hermite coe¢ cients. Thus, by solving the matrix equation, Hermite coe¢ cients are obtained. Some numerical examples are included to demonstrate the validity and applicability of the proposed technique.

Sign in / Sign up

Export Citation Format

Share Document