The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to first-order ODEs are are exhaustively described. As examples, properties of singular reduction operators of (1+ 1)-dimensional evolution and wave equations are s...

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

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 ...

This paper deals with linear stochastic partial differential equations variable coefficients driven by Lévy white noise. First, an existence theorem for integral transforms of noise is derived and the generalized mild solutions second order elliptic proved. Further, electric Schrödinger operator different potential functions V discussed.

<p style='text-indent:20px;'>In this paper, for a class of nonlinear implicit ordinary differential equation with variable coefficients, new approach to get the analytical singular solutions are given both first order and higher equations. Sufficient conditions on strengthened into necessary sufficient in specific case. Finally, results verified by practical examples MATLAB illustrations ...

the numerical methods are of great importance for approximating the solutions of nonlinear ordinary or partial differential equations, especially when the nonlinear differential equation under consideration faces difficulties in obtaining its exact solution. in this latter case, we usually resort to one of the efficient numerical methods. in this paper, the chebyshev collocation method is sugge...