English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

A new symbolic algorithmic implementation of the functional-discrete (FD-)method is developed and justified for the solution of fourth orderSturm--Liouville problem on a finite interval in the Hilbert space. Theeigenvalue problem for the fourth order ordinary differential equation withpolynomial coefficients is investigated. The sufficient conditions of anexponential convergence rate of the proposed approach are received. Theobtained estimates of the absolute errors of FD-method significantly improvethe accuracy of the estimates obtained earlier by I.P~Gavrilyuk, V.L.~Makarovand A.M.~Popov in 2010. Our algorithm is symbolic and operates with thedecomposition coefficients of the eigenfunction corrections in some basis. Thenumber of summands in these decompositions depends on the degree of thepotential coefficients and the correction number. Our method uses only thealgebraic operations and basic operations on $(2\times 1)$ column vectors and$(2\times 2)$ matrices. The proposed approach does not require solving anyboundary value problems and computations of any integrals, unlike the previousvariants of FD-method by I.P.~Gavrilyuk, V.L.~Makarov, A.M.~Popov andN.M.~Romaniuk in 2010 and 2017. The corrections to eigenpairs are computedexactly as analytical expressions, and there are no rounding errors. Thenumerical examples illustrate the theoretical results. The numerical resultsobtained with the FD-method are compared with the numerical test resultsobtained with other existing numerical techniques.

journal of computational and applied mathematics

Exponentially convergent symbolic algorithm of the functional-discrete  method for the fourth order Sturm-Liouville problems with polynomial  coefficients