scholarly journals A fully discrete Galerkin method for Abel-type integral equations

2018 ◽  
Vol 44 (5) ◽  
pp. 1601-1626 ◽  
Author(s):  
Urs Vögeli ◽  
Khadijeh Nedaiasl ◽  
Stefan A. Sauter
Keyword(s):  
Galerkin Method ◽  
Integral Equations ◽  
Fully Discrete ◽  
Type Integral ◽  
Discrete Galerkin Method

Supplement to The Discrete Galerkin Method for Integral Equations

1987 ◽  
Vol 48 (178) ◽  
pp. S11
Author(s):  
Kendall Atkinson ◽  
Alex Bogomolny
Keyword(s):  
Galerkin Method ◽  
Integral Equations ◽  
Discrete Galerkin 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.

Fully Discrete Galerkin Method For Fredholm Integro-Differential Equations With Weakly Singular Kernels

2008 ◽  
Vol 8 (3) ◽  
pp. 294-308 ◽  
Author(s):  
A. PEDAS ◽  
E. TAMME
Keyword(s):  
Galerkin Method ◽  
Inner Product ◽  
Discrete Version ◽  
Product Concept ◽  
Fully Discrete ◽  
Piecewise Polynomial Functions ◽  
Integration Techniques ◽  
Singular Kernels ◽  
Discrete Galerkin Method ◽  
The Galerkin Method

Abstract Approximations to a solution and its derivatives of a boundary value problem of an nth order linear Fredholm integro-differential equation with weakly sin-gular or other nonsmooth kernels have been determined. These approximations are piecewise polynomial functions on special graded grids. To find them, a fully discrete version of the Galerkin method has been constructed. This version is based on a dis-crete inner product concept and some suitable product integration techniques. Optimal global convergence estimates have been derived and a collection of numerical results of a test problem is given.

scholarly journals The discrete Galerkin method for integral equations

1987 ◽  
Vol 48 (178) ◽  
pp. 595 ◽  
Author(s):  
Kendall Atkinson ◽  
Alex Bogomolny
Keyword(s):  
Galerkin Method ◽  
Integral Equations ◽  
Discrete Galerkin Method

Fully Discrete Galerkin Method For Fredholm Integro-Differential Equations With Weakly Singular Kernels

2008 ◽  
Vol 8 (3) ◽  
pp. 207-222 ◽  
Author(s):  
H. BRUNNER
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Optimal Order ◽  
Piecewise Polynomial ◽  
Fully Discrete ◽  
Proportional Delays ◽  
Weakly Singular ◽  
Singular Kernels ◽  
Discrete Galerkin Method ◽  
Polynomial Collocation

AbstractWe analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays. It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with multiple vanishing delays this is no longer true.

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