Geodesic
Generalized finite difference method for solving two-interval Sturm-Liouville problems with jump conditions
Filomat, Tome 36 (2022) no. 13, p. 4505

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DOI

We consider a Sturm-Liouville problem defined on two disjoint intervals together with additional jump conditions across the common endpoint of these intervals. Based on Finite Difference Method (FDM) we have developed a new tecniqhue for solving such type nonstandard boundary value problems (BVP). To show applicability and effectiveness of the proposed generalization of FDM, we solved a simple but illustrative example. The obtained numerical solutions are graphically compared with the corresponding exact solutions.
DOI : 10.2298/FIL2213505C
Classification : 34A36, 34B09, 65L10, 65L12
Keywords: Finite Difference Method, jump conditions, transmission conditions, two-interval Sturm-Liouville differential equation 
Semih Çavuşoğlu; Oktay Sh Mukhtarov. Generalized finite difference method for solving two-interval Sturm-Liouville problems with jump conditions. Filomat, Tome 36 (2022) no. 13, p. 4505 . doi: 10.2298/FIL2213505C
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     author = {Semih \c{C}avu\c{s}o\u{g}lu and Oktay Sh Mukhtarov},
     title = {Generalized finite difference method for solving two-interval {Sturm-Liouville} problems with jump conditions},
     journal = {Filomat},
     pages = {4505 },
     year = {2022},
     volume = {36},
     number = {13},
     doi = {10.2298/FIL2213505C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2213505C/}
}
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