Mathematics of Computation, Vol. 59, No. 200 (Oct., 1992), pp. 403-420 (18 pages) We apply Runge-Kutta methods to linear partial differential equations of the form u t (x, t) = L (x, ∂)u(x, t) + f(x, ...

In this paper we discuss the numerical methods with second-order accuracy for solving stochastic differential equations. An unbiased sample approximation method for ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...