An efficient cubic B‐spline and bicubic B‐spline collocation method for numerical solutions of multidimensional nonlinear stochastic quadratic integral equations

2019 ◽  
Vol 43 (1) ◽  
pp. 384-397 ◽  
Author(s):  
Farshid Mirzaee ◽  
Sahar Alipour
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Numerical Solutions ◽  
Spline Collocation ◽  
B Spline ◽  
Spline Collocation Method ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

scholarly journals The exponential cubic B-spline collocation method for the Kuramoto-Sivashinsky equation

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 853-861 ◽  
Author(s):  
Ozlem Ersoy ◽  
Idiris Dag
Keyword(s):  
Collocation Method ◽  
Numerical Solutions ◽  
Spline Approximation ◽  
Algebraic Equations ◽  
Spline Collocation ◽  
Fully Integrated ◽  
B Spline ◽  
Spline Collocation Method ◽  
Sivashinsky Equation ◽  
Good Agreement

In this study the Kuramoto-Sivashinsky (KS) equation has been solved using the collocation method, based on the exponential cubic B-spline approximation together with the Crank Nicolson. KS equation is fully integrated into a linearized algebraic equations. The results of the proposed method are compared with both numerical and analytical results by studying two text problems. It is found that the simulating results are in good agreement with both exact and existing numerical solutions.

scholarly journals B-spline collocation methods for numerical solutions of the Burgers' equation

2005 ◽  
Vol 2005 (5) ◽  
pp. 521-538 ◽  
Author(s):  
Idris Dag ◽  
Dursun Irk ◽  
Ali Sahin
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Collocation Methods ◽  
Test Problems ◽  
Spline Collocation ◽  
B Spline ◽  
Spline Collocation Method ◽  
Burgers Equations

Both time- and space-splitted Burgers' equations are solved numerically. Cubic B-spline collocation method is applied to the time-splitted Burgers' equation. Quadratic B-spline collocation method is used to get numerical solution of the space-splitted Burgers' equation. The results of both schemes are compared for some test problems.

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