A quadratic monotone iteration scheme for two-point boundary value problems for ordinary differential equations. (English) Zbl 0939.34019
The method of upper and lower solutions and the method of quasilinearization are used to approximate the unique solution to the boundary value problem
\[
x''(t) = f(t,x(t),x'(t)), \;0 \leq t \leq 1, \;x(0) = a, \;x(1) = b,
\]
where the function \(f\) is continuous. The main contribution of the paper is that the authors extend some previous works to the case when \(f\) depends on \(x'\).
Reviewer: Antonio Cañada (Granada)
MSC:
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
Keywords:
boundary value problems; ordinary differential equations; second-order equations; upper and lower solutions; quasilinearization method; iteration schemeReferences:
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