Numerical methods for differential and integral equations are indispensable in modern applied mathematics and engineering, offering tools to approximate complex physical phenomena where analytical ...

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 ...

In this paper, we prove the general invertibility theorem for non-local pseudo-differential operators and using this, we establish the theorems of analytic continuation and of existence of holomorphic ...

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 ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...