In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...

The solution of differential equations is an important problem that arises in a host of areas. Many differential equations are too difficult to solve in closed form. Instead, it becomes necessary to employ numerical techniques. Differential equations have a major application in understanding physical systems that involve aerodynamics, fluid dynamics, thermodynamics, heat diffusion, mechanical o...

We study the linearization of a class of Liénard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is not ...

If T⃗ denotes a vector tangent to C at t,x,u then the direction numbers of T⃗ must be a,b, f. But then (1.2) implies that T⃗ n⃗, which is to say, T⃗ lies in the tangent plane to the surface S. But if T⃗ lies in the tangent plane, then C must lie in S. Evidently, solution curves of (1.2) lie in the solution surface S associated with (1.2). Such curves are called characteristic curves for (1.2). W...

In this paper we introduce a new method for solving partial and ordinary differential equations with large first, second and third derivatives of the solution in some part of the domain using the finite element technique (here called the Galerkin-Gokhman method). The method is based on the application of the Galerkin method to a modified differential equation. The exact solution of the modified...

Abstract: In this paper , for the nonlinear Cahn-Hilliard equation, we give its symmetry group by the approximate generalized conditional symmetry. As the application of approximate generalized conditional symmetry, the initial-value problem of the partial differential equations can be reduced to perturbed initial-value problem for a system of perturbed first-order ordinary differential equatio...

Motivated by several works on ordinary differential equations, we are interested in the asymptotic stability of intermittently controlled partial differential equations. We give a condition of asymptotic stability for second-order evolution equations uniformly damped by an on/off feedback. This result extends to the case of partial differential equations a previous result of R. A. Smith concern...

In this paper we present a procedure for solving first-order autonomous algebraic partial differential equations in an arbitrary number of variables. The method uses rational parametrizations of algebraic (hyper)surfaces and generalizes a similar procedure for first-order autonomous ordinary differential equations. In particular we are interested in rational solutions and present certain classe...