The use of continuously imbedded Runge-Kutta-Sarafyan methods for the solution of ordinary differential equations with either time-dependent or state-dependent delays is discc. It is shown how to get reliable solutions for such problems in a manner that does not require that the effect of the local approximation error be considered separately from the IocaI integration error. It is aIso shown h...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

This research work presents a new evolutionary optimization algorithm, EVO-RUNGE-KUTTA in theoretical mathematics with applications in scientific computing. We illustrate the application of EVO-RUNGE-KUTTA, a two-phase optimization algorithm, to a problem of pure algebra, the study of the parameterization of an algebraic variety, an open problem in algebra. Results show the design and optimizat...