On Approximate Solutions of Second-Order Linear Partial Differential Equations
نویسندگان
چکیده
منابع مشابه
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...
متن کاملOn 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
متن کاملC-approximate Solutions of Second-order Singular Ordinary Differential Equations
In this work a new method is developed to obtain C1-approximate solutions of initial and boundary-value problems generated from a one parameter second order singular ordinary differential equation. Information about the order of approximation is also given by introducing the so called growth index of a function. Conditions are given for the existence of such approximations for initial and bound...
متن کاملOn 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...
متن کاملNonrectifiable Oscillatory Solutions of Second Order Linear Differential Equations
The second order linear differential equation (p(x)y′)′ + q(x)y = 0 , x ∈ (0, x0] is considered, where p, q ∈ C1(0, x0], p(x) > 0, q(x) > 0 for x ∈ (0, x0]. Sufficient conditions are established for every nontrivial solutions to be nonrectifiable oscillatory near x = 0 without the Hartman–Wintner condition.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2012
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2012.39148