A Collocation Method for Two-Point Boundary Value Problems,
John H. Ahlberg,T. Ito +1 more
TL;DR: The problem is analyzed in terms of cubic splines first and then extended to the use of quintic and septic splines to numerically solve two-point boundary-value problems.
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Abstract: : The report is concerned with the use of collocation by splines to numerically solve two-point boundary-value problems. The problem is analyzed in terms of cubic splines first and then extended to the use of quintic and septic splines. Consideration is given both to convergences as the mesh is refined and to the bandwidth of the matrices involved. Comparisons are made to a similar approach using the Galerkin method rather than collocation. (Author)
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Citations
Quadratic spline collocation methods for elliptic partial differential equations
TL;DR: In this article, the authors considered Quadratic Spline Collocation (QSC) methods for linear second-order elliptic Partial Differential Equations (PDEs) and derived O(h 3−j) global error bounds for the first derivative.
Redefined cubic B-splines collocation method for solving convection–diffusion equations
R. C. Mittal,R.K. Jain +1 more
TL;DR: In this paper, a collocation method based on redefined cubic B-splines basis functions for solving convection-diffusion equation with Dirichlet's type boundary conditions is discussed and shown that it is unconditionally stable.
61
Cubic splines collocation methods for unilateral problems
TL;DR: In this paper, numerical experience on the use of variational inequalities and cubic splines collocation technique to obtain approximate solution to a class of unilateral boundary value problems of elasticity, like those describing the equilbrium configuration of an elastic string stretched over an elastic obstacle.
55
Cubic spline method for solving two-point boundary-value problems
Eisa A. Al-Said
- 01 Sep 1998
TL;DR: In this paper, uniform cubic spline polynomials are used to derive consistency relations and these relations are then used to develop a numerical method for computing smooth approximations to the solution and its first, second as well as third derivatives for a second order boundary value problem.
53
Troesch’s problem: A B-spline collocation approach
Suheil A. Khuri,Ali Sayfy +1 more
TL;DR: A finite-element approach, based on cubic B-spline collocation, is presented for the numerical solution of Troesch’s problem and it is observed that the results obtained are quite satisfactory and accurate, and the method is applicable for a wide range of cases when contrasted with other available solutions.
52
References
The theory of splines and their applications
J. H. Ahlberg,E. N. Nilson,J. L. Walsh +2 more
- 01 Jan 1967
2K
A collocation method for boundary value problems
TL;DR: Collocation with piecewise polynomial functions is developed as a method for solving two-point boundary value problems in this paper, and convergence is shown for a general class of linear problems and a rather broad class of nonlinear problems.
350
Piecewise Cubic Interpolation and Two-Point Boundary Problems
TL;DR: Cubic splines are employed, experimentally, to approximate to the solution of a simple two-point boundary value problem for a linear ordinary differential equation, and results are encouraging.
197