Numerical solution of integral equations by using combination of Spline-collocation method and Lagrange interpolation

2006 ◽  
Vol 175 (2) ◽  
pp. 1235-1244 ◽  
Author(s):  
K. Maleknejad ◽  
H. Derili
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Lagrange Interpolation ◽  
Spline Collocation ◽  
Spline Collocation Method

scholarly journals Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
R. C. Mittal ◽  
Rachna Bhatia
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Gordon Equation ◽  
Spline Collocation ◽  
Sine Gordon Equation ◽  
B Spline ◽  
Spline Collocation Method ◽  
B Splines ◽  
Spline Basis ◽  
The Given

Modified cubic B-spline collocation method is discussed for the numerical solution of one-dimensional nonlinear sine-Gordon equation. The method is based on collocation of modified cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. The given equation is decomposed into a system of equations and modified cubic B-spline basis functions have been used for spatial variable and its derivatives, which gives results in amenable system of ordinary differential equations. The resulting system of equation has subsequently been solved by SSP-RK54 scheme. The efficacy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and are in good agreement with earlier studies.

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

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