We study the Cauchy problem for 22 semilinear and quasilinear hyperbolic systems with a singular relaxation term. Special comparison and compactness properties are established by assuming the subcharacteristic condition. Therefore we can prove the convergence to equilibrium of the solutions of these problems as the singular perturbation parameter tends to zero. This research was strongly motiva...

Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...

We extend the perturbation theory of Vǐsik, Ljusternik and Lidskĭı for eigenvalues of matrices, using methods of min-plus algebra. We show that the asymptotics of the eigenvalues of a perturbed matrix is governed by certain discrete optimisation problems, from which we derive new perturbation formulæ, extending the classical ones and solving cases which where singular in previous approaches. Ou...

In this article, we consider rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non-C0 rectangular Morley element is uniformly convergent in the energy norm with respect to the perturbation parameter. We also propose a C0 extended high order rectangular Morley element and prove the uniform convergence. Finally, we do some numerical expe...

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...

In this paper, we consider how eigenvalues of a matrix A change when it is perturbed to e A = D 1AD2 and how singular values of a (nonsquare) matrix B change when it is perturbed to e B = D 1BD2, where D1 and D2 are assumed to be close to unitary matrices of suitable dimensions. We have been able to generalize many well-known perturbation theorems, including Ho man-Wielandt theorem and Weyl-Lid...

Using the methods of mathematical analysis and computer algebra, we developed a new reliable algorithm of initial-value method for solving nonlinear singular perturbation problems. To mechanize the algorithm a MatLab procedure called IVPHZ was established. The IVPHZ can handle problems with one or two boundary layers as well as problems with an internal shock layer. Testing of the IVPHZ was mad...

in this paper, we use modified laplace decomposition method to solving initial value problems (ivp) of the second order ordinary differential equations. theproposed method can be applied to linear and nonlinearproblems