Adaptive techniques for spline collocation

DOI10.1007/s00607-005-0141-3zbMath1086.65077OpenAlexW2146228093MaRDI QIDQ817037

Kit Sun Ng, Christina C. Christara

Publication date: 2 March 2006

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-005-0141-3

zbMATH Keywords

numerical resultssingular perturbationerror boundsspline interpolationboundary layeroptimal order of convergenceerror estimatoradaptive gridinterior layersgrid size estimatorsecond-order two-point boundary value problemSpline collocation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (14)

Modified nodal cubic spline collocation for elliptic equations ⋮ Self-adjoint singularly perturbed second-order two-point boundary value problems: a patching approach ⋮ A twofold spline Chebyshev linearization approach for a class of singular second-order nonlinear differential equations ⋮ The boundary layer problem: a fourth-order adaptive collocation approach ⋮ Automatic grid control in adaptive BVP solvers ⋮ Troesch's problem: a B-spline collocation approach ⋮ Quartic B-spline collocation method for fifth order boundary value problems ⋮ Adaptivity and computational complexity in the numerical solution of ODEs ⋮ A Lagrange-quadratic spline optimal collocation method for the time tempered fractional diffusion equation ⋮ Quadratic spline collocation for one-dimensional linear parabolic partial differential equations ⋮ A mixed decomposition-spline approach for the numerical solution of a class of singular boundary value problems ⋮ A new superconvergent method for systems of nonlinear singular boundary value problems ⋮ NUMERICAL SOLUTION OF A CLASS OF NONLINEAR SYSTEM OF SECOND-ORDER BOUNDARY-VALUE PROBLEMS: A FOURTH-ORDER CUBIC SPLINE APPROACH ⋮ Optimal quadratic and cubic spline collocation on nonuniform partitions

Uses Software

• COLNEW

Cites Work

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• Optimal quadratic and cubic spline collocation on nonuniform partitions
• Grading Functions and Mesh Redistribution
• A New Basis Implementation for a Mixed Order Boundary Value ODE Solver
• Monotone Piecewise Cubic Interpolation
• On Selection of Equidistributing Meshes for Two-Point Boundary-Value Problems
• Moving Mesh Strategy Based on a Gradient Flow Equation for Two-Dimensional Problems

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