An efficient cubic B‐spline and bicubic B‐spline collocation method for numerical solutions of multidimensional nonlinear stochastic quadratic integral equations
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.
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.
The exponential cubic B-spline collocation method for the Kuramoto-Sivashinsky equation