On Generalized Growth of Analytic Functions Solutions of Linear Homogeneous Partial Differential Equation of Second Order

On Approximate Solutions of Second-Order Linear Partial Differential Equations

In this paper, a Chebyshev polynomial approximation for the solution of second-order partial differential equations with two variables and variable coefficients is given. Also, Chebyshev matrix is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the partial differential equations. Hence, the result matrix equation can be solved and approximate va...

Analytic Solutions of a Second-Order Functional Differential Equation

On Second Order Homogeneous Linear Differential Equations with Liouvillian Solutions

We determine all minimal polynomials for second order homogeneous linear diierential equations with algebraic solutions decomposed into in-variants and we show how easily one can recover the known conditions on diierential Galois groups 12,19,25] using invariant theory. Applying these conditions and the diierential invariants of a diierential equation we deduce an alternative method to the algo...

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

Exact solutions of a linear fractional partial differential equation via characteristics method

‎In recent years‎, ‎many methods have been studied for solving differential equations of fractional order‎, ‎such as Lie group method, ‎invariant subspace method and numerical methods‎, ‎cite{6,5,7,8}‎. Among this‎, ‎the method of characteristics is an efficient and practical method for solving linear fractional differential equations (FDEs) of multi-order‎. In this paper we apply this method f...