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Multi-projection method for Volterra integral equations at the collocation points

Applied Mathematics Letters, 2013
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Khosrow Maleknejad
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Collocation at Gauss Points as a Discretization in Optimal Control

SIAM Journal on Control and Optimization, 1979
Collocation at Gauss points is shown to be a high order accurate discretization of certain unconstrained optimal control problems. Best possible convergence rates are established along with superconvergence results.
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A meshless point collocation treatment of transient bioheat problems

International Journal for Numerical Methods in Biomedical Engineering, 2014
SUMMARYA meshless numerical method is proposed for the solution of the transient bioheat equation in two and three dimensions. The Pennes bioheat equation is extended in order to incorporate water evaporation, tissue damage, and temperature‐dependent tissue properties during tumor ablation.
G C, Bourantas, V C, Loukopoulos, V N, Burganos, G C, Nikiforidis   +3 more
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The Richardson Extrapolation Process with a Harmonic Sequence of Collocation Points

SIAM Journal on Numerical Analysis, 2000
The author studies the problem: Let a function \(A(y)\) be known and hence computable for \(00\), the variable \(y\) being continuous or discrete. The author assumes that \(A(y)\) has an asymptotic expansion of the form \[ A(y)\sim A+ \sum_{k=1}^\infty \alpha_k y^{\sigma_k} \quad\text{as}\quad y\to 0+, \] where \(\sigma_k\) are known scalars satisfying
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On a misconception involving point collocation and the Rayleigh hypothesis

IEEE Transactions on Antennas and Propagation, 1996
Summary: It is shown that the Rayleigh hypothesis does not govern convergence of the simple point collocation approach to the numerical solution of scattering by a sinusoidal grating. A recently developed numerical technique, interval arithmetic, is employed to perform some decisive numerical experiments which not only support but guarantee the ...
Christiansen, Søren, Kleinman, Ralph E.
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Collocation by L-Splines at Transformed Gaussian Points

SIAM Journal on Numerical Analysis, 1984
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Collocation for Two-Point Boundary Value Problems Revisited

SIAM Journal on Numerical Analysis, 1986
Collocation methods for two-point boundary value problems for higher differential equations are considered. By using appropriate monomial bases, these methods are related to corresponding one-step schemes for first order systems of differential equations.
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Errors in Iteration Points in Oscillatory State for Chebyshev Collocation Points

1999
When the Chebyshev collocation point is calculated by Newton’s iteration process, the round-off errors of iteration points are difficult to analyze. The equation which determines the unknown round-off error is obtained for the iteration point under the condition that the iteration point is stationary.
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Maximum principle and convergence analysis for the meshfree point collocation method

SIAM Journal on Numerical Analysis, 2006
The discrete Laplacian operator is considered in the sense of the meshfree point collocation method which will be called the strong meshfree Laplacian operator. To define the strong meshfree Laplacian operator, we use the fast version of the generalized moving least square approximation, which can calculate the approximated derivatives of shape ...
Do Wan Kim, Wing Kam Liu
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Nonoverlapping domain decomposition with cross points for orthogonal spline collocation

Journal of Numerical Mathematics, 2008
A nonoverlapping domain decomposition approach with uniform and matching grids is used to define and compute the orthogonal spline collocation solution of the Dirichlet boundary-value problem for Poisson's equation on a square partitioned into four squares.
Bernard Bialecki, Maksymilian Dryja
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