scholarly journals Fully discrete collocation method for weakly singular integral equations

2001 ◽  
Vol 50 (3) ◽  
pp. 133
Author(s):  
E Tamme
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Fully Discrete ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations

scholarly journals ON FULLY DISCRETE COLLOCATION METHODS FOR SOLVING WEAKLY SINGULAR INTEGRAL EQUATIONS

2009 ◽  
Vol 14 (1) ◽  
pp. 69-78 ◽  
Author(s):  
Raul Kangro ◽  
Inga Kangro
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Collocation Methods ◽  
Quadrature Formulas ◽  
Nonuniform Grids ◽  
Fully Discrete ◽  
Straightforward Application ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations

A popular class of methods for solving weakly singular integral equations is the class of piecewise polynomial collocation methods. In order to implement those methods one has to compute exactly certain integrals that determine the linear system to be solved. Unfortunately those integrals usually cannot be computed exactly and even when analytic formulas exist, their straightforward application may cause unacceptable roundoff errors resulting in apparent instability of those methods in the case of highly nonuniform grids. In this paper fully discrete analogs of the collocation methods, where integrals are replaced by quadrature formulas, are considered, corresponding error estimates are derived.

scholarly journals POLYNOMIAL SPLINE COLLOCATION METHOD FOR NONLINEAR TWO‐DIMENSIONAL WEAKLY SINGULAR INTEGRAL EQUATIONS

1997 ◽  
Vol 2 (1) ◽  
pp. 122-129 ◽  
Author(s):  
Arvet Pedas
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Polynomial Spline ◽  
Two Dimensional ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations

„Polynomial spline collocation method for nonlinear two‐dimensional weakly singular integral equations" Mathematical Modelling Analysis, 2(1), p. 122-129

scholarly journals QUADRATIC SPLINE COLLOCATION METHOD FOR WEAKLY SINGULAR INTEGRAL EQUATIONS AND CORRESPONDING EIGENVALUE PROBLEM

2002 ◽  
Vol 7 (2) ◽  
pp. 285-296 ◽  
Author(s):  
R. Pallav ◽  
A. Pedas
Keyword(s):  
Eigenvalue Problem ◽  
Integral Equations ◽  
Collocation Method ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Spline Collocation ◽  
Quadratic Spline ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations ◽  
Quadratic Spline Collocation

A quadratic spline collocation method for the numerical solution of weakly singular Fredholm integral equations of the second kind and corresponding eigenvalue problem is constructed. Using quasi‐uniform and special graded grids, the rate of convergence of proposed numerical schemes is studied theoretically and numerically. Key words: weakly singular integral equations, collocation method, quadratic splines.

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