Open AccessNumerical Method of the Line for Solving One Dimensional Initial- Boundary Singularly Perturbed Burger Equation
Author(s) -
Kedir Aliyi,
Hailu Muleta
Publication year - 2021
Publication title -
indian journal of advanced mathematics
Language(s) - English
Resource type - Journals
ISSN - 2582-8932
DOI - 10.35940/ijam.b1103.101221
Subject(s) - mathematics , discretization , mathematical analysis , singular perturbation , numerical analysis , ordinary differential equation , boundary value problem , von neumann stability analysis , rate of convergence , variable (mathematics) , neumann boundary condition , differential equation , channel (broadcasting) , engineering , electrical engineering
In this Research Method of Line is used tofind the approximation solution of one dimensionalsingularly perturbed Burger equation given with initial andboundary conditions. First, the given solution domain isdiscretized and the derivative involving the spatialvariablexis replaced into the functional values at each gridpoints by using the central finite difference method. Then,the resulting first-order linear ordinary differentialequation is solved by the fifth-order Runge-Kutta method.To validate the applicability of the proposed method, onemodel example is considered and solved for different valuesof the perturbation parameter ‘’ and mesh sizes in thedirection of the temporal variable, t. Numerical results arepresented in tables in terms of Maximum point-wise error,N t , Eand rate of convergence,N t , P. The stability of thisnew class of Numerical method is also investigated by usingVon Neumann stability analysis techniques. The numericalresults presented in tables and graphs confirm that theapproximate solution is in good agreement with the exactsolution.