Abstract
Abstract A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are exhibited to verify the efficiency and accuracy of the proposed technique. In this sequel, the obtained error was shown between the proposed technique, Chebyshev wavelets, and Legendre wavelets. The results display that this technique is accurate.
Highlights
IntroductionWhere λ > 0 is a physical parameter and Ω ∈ RN is a bounded domain. one may focus on the boundary value problem and initial value problem of Bratu’s problem
In this sequel, Liouville-Bratu-Gelfand equation is considered∆u + λeu = 0, x ∈ Ω, u = 0, x ∈ ∂Ω, (1)where λ > 0 is a physical parameter and Ω ∈ RN is a bounded domain
The obtained error was shown between the proposed technique, Chebyshev wavelets, and Legendre wavelets
Summary
Where λ > 0 is a physical parameter and Ω ∈ RN is a bounded domain. one may focus on the boundary value problem and initial value problem of Bratu’s problem. The critical value λc was calculated in [2,3,4] and found to be λc = 3.513830719 This solution displays a bifurcation pattern, which only characterizes nonlinear differential equations. We have the following Bratu’s boundary value problem:. The way to solve a boundary or initial value problem consists of computing first the general solution to the differential equation and secondly of finding the arbitrary parameters by applying the boundary or initial conditions (see [21]). Zheng et al [29] proposed the utilization of control points of the Bezier curve for solving differential equations numerically. To solve delay differential equations, the Bezier control points strategy is utilized in [30].
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