A Fully Discrete Galerkin Method for Integral and Pseudo differential Equations on Closed Curves

1995 ◽  
Vol 14 (3) ◽  
pp. 593-622
Author(s):  
O. Kelle ◽  
Gennadi Vainikko
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Closed Curves ◽  
Fully Discrete ◽  
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.

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 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
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