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 acc
Polynomial approximate solutions with a priori error bounds of first-order quasi-linear initial-value partial differential problems
✍ Scribed by L. Jódar; M.D. Roselló
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 665 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0895-7177
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✦ Synopsis
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 accuracy.
📜 SIMILAR VOLUMES
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