Classroom Note:
Calculation of Weights in Finite Difference Formulas

We consider variations of the Adams--Bashforth, backward differentiation, and Runge--Kutta families of time integrators to solve systems of linear wave equations on uniform, time-staggered grids. These methods are found to have smaller local truncation ...

The initial value problems of nonlinear ordinary differential equations which contain stiff and nonstiff terms often arise from many applications. In order to reduce the computation cost, implicit-explicit (IMEX) methods are often applied to these ...

Numerical integration methods for nonlinear differential-algebraic equations (DAEs) in strangeness-free form are studied. In particular, half-explicit methods based on popular explicit methods like one-leg methods, linear multistep methods, and Runge-...