Numerical experiments involving galerkin and collocation methods for linear integral equations of the first kind

1983 ◽  
Vol 49 (3) ◽  
pp. 465-477 ◽  
Author(s):  
Richard C Allen ◽  
W Robert Boland ◽  
G.Milton Wing
Keyword(s):  
Integral Equations ◽  
Numerical Experiments ◽  
Collocation Methods ◽  
Linear Integral ◽  
Galerkin And Collocation Methods ◽  
Linear Integral Equations

On Projective Methods of Approximate Solution of Singular Integral Equations

1996 ◽  
Vol 3 (5) ◽  
pp. 457-474
Author(s):  
A. Jishkariani ◽  
G. Khvedelidze
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Collocation Methods ◽  
Projective Methods ◽  
Galerkin And Collocation Methods

Abstract The estimate for the rate of convergence of approximate projective methods with one iteration is established for one class of singular integral equations. The Bubnov–Galerkin and collocation methods are investigated.

scholarly journals On the numerical solutions for nonlinear Volterra-Fredholm integral equations

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Parviz Darania ◽  
Saeed Pishbin
Keyword(s):  
Nonlinear System ◽  
Integral Equations ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Coefficient Matrix ◽  
Collocation Methods ◽  
Fredholm Integral Equations ◽  
Stability Estimates ◽  
Lower Triangular ◽  
Theoretical Results

In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an efficient implementation. Convergence analysis and linear stability estimates are investigated. Finally numerical experiments are given, which confirm our theoretical results.

scholarly journals On Solvability Conditions for a Certain Conjugation Problem

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 234
Author(s):  
Vladimir Vasilyev ◽  
Nikolai Eberlein
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Mellin Transform ◽  
Algebraic Equations ◽  
Conjugation Problem ◽  
Solvability Conditions ◽  
Linear Algebraic Equations ◽  
Linear Integral ◽  
Linear Integral Equations

We study a certain conjugation problem for a pair of elliptic pseudo-differential equations with homogeneous symbols inside and outside of a plane sector. The solution is sought in corresponding Sobolev–Slobodetskii spaces. Using the wave factorization concept for elliptic symbols, we derive a general solution of the conjugation problem. Adding some complementary conditions, we obtain a system of linear integral equations. If the symbols are homogeneous, then we can apply the Mellin transform to such a system to reduce it to a system of linear algebraic equations with respect to unknown functions.

On the location of the Weyl circles

1981 ◽  
Vol 88 (3-4) ◽  
pp. 345-356 ◽  
Author(s):  
F. V. Atkinson
Keyword(s):  
Integral Equations ◽  
Complex Plane ◽  
Riccati Equations ◽  
Sturm Liouville ◽  
Linear Integral ◽  
Linear Integral Equations

SynopsisThe paper deals with explicit estimates concerning certain circles in the complex plane which were associated with Sturm–Liouville problems by H. Weyl. By the use of Riccati equations instead of linear integral equations, improvements are obtained for results of Everitt and Halvorsen concerning the behaviour of the Titchmarsh–Weyl m-coefficient.

Integral equations and relations for Lamé functions and ellipsoidal wave functions

1968 ◽  
Vol 64 (1) ◽  
pp. 113-126 ◽  
Author(s):  
B. D. Sleeman
Keyword(s):  
Wave Function ◽  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Function Theory ◽  
Natural Generalization ◽  
Wave Functions ◽  
Linear Integral ◽  
First Time ◽  
Linear Integral Equations

AbstractNon-linear integral equations and relations, whose nuclei in all cases is the ‘potential’ Green's function, satisfied by Lamé polynomials and Lamé functions of the second kind are discussed. For these functions certain techniques of analysis are described and these find their natural generalization in ellipsoidal wave-function theory. Here similar integral equations are constructed for ellipsoidal wave functions of the first and third kinds, the nucleus in each case now being the ‘free space’ Green's function. The presence of ellipsoidal wave functions of the second kind is noted for the first time. Certain possible generalizations of the techniques and ideas involved in this paper are also discussed.

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