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 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.

Single-Term Walsh Series Direct Method for the Solution of Nonlinear Problems in the Calculus of Variations

2004 ◽  
Vol 10 (7) ◽  
pp. 1071-1081 ◽  
Author(s):  
M. Razzaghi ◽  
B. Sepehrian
Keyword(s):  
Calculus Of Variations ◽  
Nonlinear Problem ◽  
Direct Method ◽  
Nonlinear Problems ◽  
Variational Problems ◽  
Walsh Series ◽  
Algebraic Equations ◽  
Brachistochrone Problem ◽  
Single Term ◽  
A Direct Method

A direct method for solving variational problems using single-term Walsh series is presented. Two nonlinear examples are considered. In the first example the classical brachistochrone problem is examined. and in the second example a higher-order nonlinear problem is considered. The properties of single-term Walsh series are given and are utilized to reduce the calculus of variations problems to the solution of algebraic equations. The method is general, easy to implement and yields accurate results.

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

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