This paper is concerned with time-stepping numerical methods for computing sti semi-discrete systems of ordinary di erential equations for transient hypersonic ows with thermo-chemical nonequilibrium. The sti ness of the equations is mainly caused by the viscous ux terms across the boundary layers and by the source terms modeling nite-rate thermo-chemical processes. Implicit methods are needed ...

In recent years, Fuzzy differential equations are very useful indifferent sciences such as physics, chemistry, biology and economy. It should be noted, that if the equations that appear to be uncertain, then take help of fuzzy logic at these equations. Considering that most of the time analytic solution of such equations and finding an exact solution has either high complexity or cannot be solv...

In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.

Game theory is concerned with optimization problems involving several players with conicting interests. Di erential games are an interesting area inside this eld in which the problem is formulated by means of dynamical systems. In spite that the theoretical solution of di erential games is well known, faced with large-scale, complex systems, analytical or, even, numerical methods are not usuall...

The problem of simultaneous reduction of real matrices by either orthogo nal similarity or orthogonal equivalence transformations is considered Based on the Jacobi idea of minimizing the sum of squares of the complementary part of the desired form to which matrices are reduced the projected gradi ent method is used in this paper It is shown that the projected gradient of the objective function ...

The stabilized march technique is extended to nonlinear two-point boundary value problems via a new Generalized Brent Method for systems of nonlinear algebraic equations. The resulting algorithms can be used to solve systems of nonlinear rst-order ordinary di erential equations under partially separated nonlinear boundary conditions economically. Numerical results which compare the nonlinear st...

Flame sheet problems are on the natural route to the numerical solution of detailed chemistry, laminar di usion ames, which, in turn, are important in many engineering applications. In order to model the ame structure more accurately, we use the vorticity-velocity formulation of the uid ow equations instead of the more traditional stream function-vorticity approach. The numerical solution of th...

A 2nd-order, L-stable Rosenbrock method from the eld of sti ordinary di erential equations is studied for application to atmospheric dispersion problems describing photochemistry, advective and turbulent di usive transport. Partial di erential equation problems of this type occur in the eld of air pollution modelling. The focal point of the paper is to examine the Rosenbrock method for reliable...

Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order, "-dependent parabolic partial di erential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the fundamental solution of an \averaged" parabolic equation, we bring forth a novel approach to compar...

We study the existence of periodic solutions for a nonlinear system of n-th order di erential equations on time-scales. Assuming a suitable Nirenberg type condition, we prove the existence of at least one solution of the problem using Mawhin's coincidence degree.