The efficiency with which the numerical solution of ordinary differential equations can be generated depends to a large extent on the effectiveness of the stepsize adjustment strategy that is used. A new strategy for carrying out this critical task is proposed in this paper. A distinctive...

Past research demonstrated that the Newton method coupled with Krylov subspace iterative methods is more efficient than the Newton method coupled with Gaussian elimination when used to solve the corrector equation in stiff systems of Ordinary Differential Equations (ODEs)-with large and sparse...

The application of spectral collocation methods to second- and fourth-order boundary value problems in rectangular domains leads to systems of n algebraic equations in n unknowns. Under certain conditions, it may be shown that the systems obtained when imposing the boundary conditions in the...

A generalized Lagrangian formulation of the shallow water equations in conservation law form using the Lagrangian distance and stream function as independent variables is described. The resulting system is fully hyperbolic and renders the flux vector continuous at tangential discontinuities. A...

The locus drawn by a car travelling at a low speed can be expressed by using circular arcs. This principle is applied to simulate travelling of an autonomous mobile robot with four wheels (Ohkita et al. (1990)). With this fact, it is shown that, by combining simple fuzzy control rules, the robot...