Computable error bounds with improved applicability conditions for collocation methods.

Ahmed, A.H.

Displaying similar documents to “Computable error bounds with improved applicability conditions for collocation methods.”

Computable error bounds for collocation methods.

Ahmed, A.H. (1995)

International Journal of Mathematics and Mathematical Sciences

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Complementarity - the way towards guaranteed error estimates

Vejchodský, Tomáš

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This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamental properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples.

Improving the Accuracy of Collocation Solutions of Volterra Integral Equations of the First Kind by Local Interpolation.

P.P.B Eggermont (1986)

Numerische Mathematik

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Error Bounds for Computed Eigenvalues and Eigenvectors. II

T. Yamamoto (1982)

Numerische Mathematik

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Two-sided bounds of the discretization error for finite elements

Michal Křížek, Hans-Goerg Roos, Wei Chen (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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We derive an optimal lower bound of the interpolation error for linear finite elements on a bounded two-dimensional domain. Using the supercloseness between the linear interpolant of the true solution of an elliptic problem and its finite element solution on uniform partitions, we further obtain two-sided bounds of the discretization error by means of the interpolation error. Two-sided bounds for bilinear finite elements are given as well. Numerical tests illustrate our theoretical analysis. ...

Uniformly convergent schemes for singularly perturbed differential equations based on collocation methods.

Konate, Dialla (2000)

International Journal of Mathematics and Mathematical Sciences

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A unified approach to singular problems arising in the membrane theory

Irena Rachůnková, Gernot Pulverer, Ewa B. Weinmüller (2010)

Applications of Mathematics

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We consider the singular boundary value problem ${(t^{n} u^{'} (t))}^{'} + t^{n} f (t, u (t)) = 0, lim_{t \to 0 +} t^{n} u^{'} (t) = 0, a_{0} u (1) + a_{1} u^{'} (1 -) = A,$ where $f (t, x)$ is a given continuous function defined on the set $(0, 1] \times (0, \infty)$ which can have a time singularity at $t = 0$ and a space singularity at $x = 0$ . Moreover, $n \in ℕ$ , $n \geq 2$ , and $a_{0}$ , $a_{1}$ , $A$ are real constants such that $a_{0} \in (0, \infty)$ , whereas $a_{1}, A \in [0, \infty)$ . The main aim of this paper is to discuss the existence of solutions to the above problem and apply the general results to cover certain classes of singular problems arising in the theory of shallow membrane caps, where we are especially interested...