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Nonlinear extrapolation and two-point boundary value problems

Authors:

Richard Bellman,

Harriet Kagiwada,

Robert KalabaAuthors Info & Claims

Communications of the ACM, Volume 8, Issue 8

Pages 511 - 512

https://doi.org/10.1145/365474.365523

Published: 01 August 1965 Publication History

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Abstract

It is suggested that the convergence properties of the usual Picard successive approximation scheme may be improved through use of nonlinear extrapolation techniques. A numerical example is provided.

References

[1]

KALABA, R.E. On nonlinear differential equations, the maximum operation and monotone convergence. J. of Math. and Mech. 8 (1959), 519-574.

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[2]

SHANKS, D. Non-linear transformations of divergent and slowly convergent sequences. J. Math. and Phys. 34 (1955), 1-42.

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[3]

BELLMAN, R., AND KALABA, R. E. Quasilinearization and Nonlinear Boundary-value Problems. American Elsevier Co., 1965.

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Dhlamini MZondo KMondal HSibanda PShaw SMotsa SMkhatshwa MMagodora M(2023)Second-grade bioconvection flow of a nanofluid with slip convective boundary conditionsPramana10.1007/s12043-023-02676-097:4Online publication date: 27-Nov-2023
https://doi.org/10.1007/s12043-023-02676-0
Kurbatova GKlemeshev V(2022)Mathematical Apparatus for Detecting Leakage in Gas PipelinesMathematical Models and Computer Simulations10.1134/S207004822202009014:2(203-212)Online publication date: 5-Apr-2022
https://doi.org/10.1134/S2070048222020090
Khalil HKhalil MHashim IAgarwal P(2021)Extension of Operational Matrix Technique for the Solution of Nonlinear System of Caputo Fractional Differential Equations Subjected to Integral Type Boundary ConstrainsEntropy10.3390/e2309115423:9(1154)Online publication date: 2-Sep-2021
https://doi.org/10.3390/e23091154
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Index Terms

Nonlinear extrapolation and two-point boundary value problems
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
    2. Numerical analysis
      1. Interpolation

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Published In

Communications of the ACM Volume 8, Issue 8

Aug. 1965

67 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/365474

Editor:
C. C. Gotlieb
Univ. of Toronto, Toront, Ont., Canada

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Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 August 1965

Published in CACM Volume 8, Issue 8

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Dhlamini MZondo KMondal HSibanda PShaw SMotsa SMkhatshwa MMagodora M(2023)Second-grade bioconvection flow of a nanofluid with slip convective boundary conditionsPramana10.1007/s12043-023-02676-097:4Online publication date: 27-Nov-2023
https://doi.org/10.1007/s12043-023-02676-0
Kurbatova GKlemeshev V(2022)Mathematical Apparatus for Detecting Leakage in Gas PipelinesMathematical Models and Computer Simulations10.1134/S207004822202009014:2(203-212)Online publication date: 5-Apr-2022
https://doi.org/10.1134/S2070048222020090
Khalil HKhalil MHashim IAgarwal P(2021)Extension of Operational Matrix Technique for the Solution of Nonlinear System of Caputo Fractional Differential Equations Subjected to Integral Type Boundary ConstrainsEntropy10.3390/e2309115423:9(1154)Online publication date: 2-Sep-2021
https://doi.org/10.3390/e23091154
Saritha KRajasekhar MReddy B(2018)Combined Effects of Soret and Dufour on MHD Flow of a Power-Law Fluid Over Flat Plate in Slip Flow RigimeInternational Journal of Applied Mechanics and Engineering10.2478/ijame-2018-003823:3(689-705)Online publication date: 20-Aug-2018
https://doi.org/10.2478/ijame-2018-0038
Kishan NShashidar Reddy B(2013)MHD Effects on Non-Newtonian Power-Law Fluid Past a Continuously Moving Porous Flat Plate with Heat Flux and Viscous DissipationInternational Journal of Applied Mechanics and Engineering10.2478/ijame-2013-002518:2(425-445)Online publication date: 8-Jun-2013
https://doi.org/10.2478/ijame-2013-0025
Morris P(2006)The spatial viscous instability of axisymmetric jetsJournal of Fluid Mechanics10.1017/S002211207600223177:3(511-529)Online publication date: 11-Apr-2006
https://doi.org/10.1017/S0022112076002231
Lew A(1986)Richard Bellman's contributions to computer scienceJournal of Mathematical Analysis and Applications10.1016/0022-247X(86)90146-0119:1-2(90-96)Online publication date: Oct-1986
https://doi.org/10.1016/0022-247X(86)90146-0
Sundaram KNath G(1976)Flow and heat transfer for a power-law electrically conducting fluid flowing between parallel plates under transverse magnetic field with viscous dissipationProceedings of the Indian Academy of Sciences - Section A10.1007/BF0305133983:5(188-201)Online publication date: May-1976
https://doi.org/10.1007/BF03051339
(1970)BIBLIOGRAPHYIterative Solution of Nonlinear Equations in Several Variables10.1016/B978-0-12-528550-6.50029-6(523-557)Online publication date: 1970
https://doi.org/10.1016/B978-0-12-528550-6.50029-6
Helfrich H(1969)Ein Modifiziertes Newtonsches VerfahrenFunktionalanalytische Methoden der numerischen Mathematik10.1007/978-3-0348-5838-0_7(61-70)Online publication date: 1969
https://doi.org/10.1007/978-3-0348-5838-0_7
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Recommendations

The extrapolation of Numerov's scheme for nonlinear two-point boundary value problems

A superconvergent local discontinuous Galerkin method for nonlinear two-point boundary-value problems

Multipoint Boundary-Value Solution of Two-Point Boundary-Value Problems

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