Title: Semi-Lagrangian one-step methods for two classes of time-dependent partial differential systems,
Abstract: Semi-Lagrangian methods are numerical methods designed to find approximate
solutions to particular time-dependent partial differential equations (PDEs)
that describe the advection process. We propose semi-Lagrangian one-step
methods for numerically solving initial value problems for two general systems
of partial differential equations. Along the characteristic lines of the PDEs,
we use ordinary differential equation (ODE) numerical methods to solve the
PDEs. The main benefit of our methods is the efficient achievement of high
order local truncation error through the use of Runge-Kutta methods along the
characteristics. In addition, we investigate the numerical analysis of
semi-Lagrangian methods applied to systems of PDEs: stability, convergence, and
maximum error bounds.