Fourier series direct method for variational problems. (English) Zbl 0651.49012

Summary: A direct method for solving variational problems using Fourier series is presented. An operational matrix of integration is first introduced and is utilized to reduce a variational problem to the solution of algebraic equations. Illustrative examples are also given.


49M05 Numerical methods based on necessary conditions
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
49K05 Optimality conditions for free problems in one independent variable
44A45 Classical operational calculus
Full Text: DOI


[1] DOI: 10.1007/BF00934535 · Zbl 0481.49004 · doi:10.1007/BF00934535
[2] DOI: 10.1080/00207727508941868 · Zbl 0311.93015 · doi:10.1080/00207727508941868
[3] DOI: 10.1080/0020718508961114 · Zbl 0555.93023 · doi:10.1080/0020718508961114
[4] CORRINGTON M. S., I.E.E.E. Trans. Circuit Theory 20 pp 470– (1973)
[5] DOI: 10.1080/00207728508926718 · Zbl 0568.49019 · doi:10.1080/00207728508926718
[6] DOI: 10.1080/00207178108922979 · Zbl 0464.93027 · doi:10.1080/00207178108922979
[7] DOI: 10.1080/00207178108922549 · Zbl 0469.93033 · doi:10.1080/00207178108922549
[8] DOI: 10.1080/00207728508926663 · Zbl 0558.44004 · doi:10.1080/00207728508926663
[9] SCHECHTER R. S., The Variation Method in Engineering (1967) · Zbl 0176.10001
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