High Order Data Bounded Numerical Approximations of Hyperbolic Conservation Laws

Abstract

The Construction of an ideal non-linear stable higher order numerical scheme for newlinehyperbolic conservation law has been a trending topic in the last few decades. Balancing newlinebetween high order accuracy and stability is a challenging problem, thus creates a space newlinefurther development of schemes with improved balance. newlineOne of the fundamental issues with the numerical approximation of the hyperbolic newlineconservation law has been spurious induced oscillations. In this thesis, generic three point newlineschemes for the scalar case are studied using the concept of data dependent stability to newlinedemonstrate that the induced oscillations are dependent on the initial data. Furthermore, newlineit is concluded that it is impossible to obtain an initial data independent, uniformly nonoscillatory newlinethree point scheme regardless of its accuracy newline