Decatic B‐spline collocation scheme for approximate solution of Burgers' equation
Saumya Ranjan Jena, Guesh Simretab Gebremedhin
Abstract
Abstract A decatic B‐spline collocation technique is employed to compute the numerical result of a nonlinear Burgers' equation. The nonlinear term of Burgers' equation is locally linearized using Taylor series technique. The present method is effective for the approximate solution of Burgers' with a very small value of kinematic viscosity “ a .” Some illustrated numerical experiments are taken into consideration to focus on the importance of the current work and some comparative studies are reported with others as well as with the exact solutions. The linear stability of the method is analyzed with Von Neumann technique. Application of higher‐order derivatives rather than lower‐order derivatives of the decatic B‐splines on the boundary conditions is the keynote to obtain a better approximate solution of the present method.