Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

We analyze three one parameter families of approximations and show that they are symplectic in Lagrangian sence and can be related to symplectic schemes in Hamiltonian sense by different symplectic ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

Mathematics of Computation, Vol. 49, No. 180 (Oct., 1987), pp. 523-542 (20 pages) We present Runge-Kutta methods of high accuracy for stochastic differential ...