Matlab has facilities for the numerical solution of ordinary differential equations (ODEs) of any order. In this document we first consider the solution of a first order ODE. Higher order ODEs can be solved using the same methods, with the higher order equations first having to be reformulated as a system of first order equations. Techniques for solving the first order and second order equation...

We discuss the numerical solution of linear quadratic optimal control problems for descriptor systems. The classical solution approach for these problems requires the computation of deeating subspaces of structured pencils. We extend the recently developed methods 6] for Hamiltonian matrices to the general case of embedded pencils as they arise in descriptor systems.

In this paper we propose a new solution technique for numerical solution of fractional Benney equation, a fourth degree nonlinear fractional partial differential equation with broad range of applications. The method could be described as a hybrid technique which uses advantages of both wavelets and operational matrices. Having applied the present method, fractional Benney equation is converted ...

We consider the ‘classical’ Boussinesq system of water wave theory, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a horizontal channel. (We also consider its completely symmetric analog). We discretize the initial-boundary-value problem for these systems, corresponding to homogeneous Dirichlet boundary ...

The numerical solution of a Rayleigh-Taylor instability problem where an inviscid liquid of finite depth is accelerated into a gas of semi-infinite extent is obtained by transforming the irregular flow domain into a rectangular domain by a coordinate transformation. The free surface equation is solved by a Crank-Nicolson procedure. The boundary condition at the free surface for the velocity pot...

Two eecient methods for solving generalized Lyapunov equations and their implementations in FORTRAN 77 are presented. The rst one is a generalization of the Bartels{Stewart method and the second is an extension of Ham-marling's method to generalized Lyapunov equations. Our LAPACK based subroutines are implemented in a quite exible way. They can handle the transposed equations and provide scalin...

This paper is devoted to two-dimensional diierential games. The problem of nding the set of all points for each of which the rst player guarantees the achievement of a given target set within a nite time interval under any actions of the second player is considered (the game of kind). An algorithm based on operations of constructing and sewing semipermeable curves is given. One particular nonli...

We consider the numerical solution of projected algebraic Riccati equations using Newton’s method. Such equations arise, for instance, in model reduction of descriptor systems based on positive real and bounded real balanced truncation. We also discuss the computation of low-rank Cholesky factors of the solutions of projected Riccati equations. Numerical examples are given that demonstrate the ...

This work was partially supported by The Geometry Center of the University of Minnesota and the University of Massachusetts at Amherst. The soap film problem is to minimize area, and its dual is to maximize the flux of a divergenceless bounded vector field. This paper discretizes the continuous problem and solves it numerically. This gives upper and lower bounds on the area of the globally mini...