𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Constructive polynomial approximation with a priori error bounds for nonlinear initial value differential problems

✍ Scribed by L. Jódar; A.E. Posso; H. Castejón

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
486 KB
Volume
38
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we consider an initial value problem y' = fi x, y), yi 0) = Y0, where f is a continuous function satisfying a Lipschitz condition. First, the function fix, y) is approximated by a Bernstein polynomial in two variables, Bnif; x,y), of an appropriate degree according to a prescribed accuracy. Second, by application of the Frobenius method to the initial value problem y' = B,~(f; z, y), y(O) ----Y0, an exact series solution of the latter problem is constructed. Finally, the infinite series solution is truncated in order to obtain an explicit polynomial whose error with respect to the exact solution of the original problem is less than the prescribed accuracy, in an existence and uniqueness domain which is determined in terms of the initial data. (~) 1999 Elsevier Science Ltd. All rights reserved.

📜 SIMILAR VOLUMES

Frobenius-Chebyshev polynomial approxima
Frobenius-Chebyshev polynomial approximations with a priori error bounds for nonlinear initial value differential problems
✍ B. Chen; R.Garcia Bolós; L. Jódar 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 578 KB

In this paper, we present a method for approximating the solution of initial value ordinary differential equations with a priori error bounds. The method is based on a Chebyshev perturbation of the original differential equation together with the Frobenius method for solving the equation. Chebyshev

Polynomial approximate solutions with a
Polynomial approximate solutions with a priori error bounds of first-order quasi-linear initial-value partial differential problems
✍ L. Jódar; M.D. Roselló 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 665 KB

## In this paper, we construct polynomial approximate solutions with a priori error bounds of first-order quasi-linear initial-value partial differential problems with analytic Cauchy data. After constructing a power series solution, this is appropriately truncated according with a prefixed accura

Analytic-numerical solutions with a prio
Analytic-numerical solutions with a priori error bounds for time-dependent mixed partial differential problems
✍ L. Jódar; E. Defez 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 413 KB

The aim of this paper is double. First, we point out that the hypothesis D(tl)D(t2) = D(t2)D(tl) imposed in [1] can be removed. Second, a constructive method for obtaining analyticnumerical solutions with a prefixed accuracy in a bounded domain gl(to, tl) = [0,p] x [t0,tl], for mixed problems of the