On order-reducible sinc discretizations and block-diagonal preconditioning methods for linear third-order ordinary differential equations
نویسندگان
چکیده
منابع مشابه
On order-reducible sinc discretizations and block-diagonal preconditioning methods for linear third-order ordinary differential equations
By introducing a variable substitution we transform the two-point boundary value problem of a third-order ordinary differential equation into a system of two second-order ordinary differential equations. We discretize this order-reduced system of ordinary differential equations by both sinc-collocation and sinc-Galerkin methods, and average these two discretized linear systems to obtain the tar...
متن کاملOn sinc discretization and banded preconditioning for linear third-order ordinary differential equations
Some draining or coating fluid-flow problems and problems concerning the flow of thin films of viscous fluid with a free surface can be described by third-order ordinary differential equations. In this paper, we solve the boundary value problems of such equations by sinc discretization and prove that the discrete solutions converge to the true solutions of the ordinary differential equations ex...
متن کاملOrder Ordinary Differential Equations
The DI methods for directly solving a system ofa general higher order ODEs are discussed. The convergence of the constant stepsize and constant order formulation of the DI methods is proven first before the convergencefor the variable order and stepsize case.
متن کاملApproximately $n$-order linear differential equations
We prove the generalized Hyers--Ulam stability of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.
متن کاملOn Conjugacy of High-order Linear Ordinary Differential Equations
It is shown that the differential equation u(n) = p(t)u, where n ≥ 2 and p : [a, b] → R is a summable function, is not conjugate in the segment [a, b], if for some l ∈ {1, . . . , n− 1} , α ∈]a, b[ and β ∈]α, b[ the inequalities n ≥ 2 + 1 2 (1 + (−1)n−l), (−1)n−lp(t) ≥ 0 for t ∈ [a, b],
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: Numerical Linear Algebra with Applications
سال: 2013
ISSN: 1070-5325
DOI: 10.1002/nla.1868