On the numerical schemes for Langevin-type equations | Zendy

Muzaffer Akat | Zendy; Reşat Köşker | Zendy; Ali Sırma | Zendy

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On the numerical schemes for Langevin-type equations

Author(s) -

Muzaffer Akat,

Reşat Köşker,

Ali Sırma

Publication year - 2020

Publication title -

bulletin of the karaganda university-mathematics

Language(s) - English

Resource type - Journals

eISSN - 2663-5011

pISSN - 2518-7929

DOI - 10.31489/2020m3/62-74

Subject(s) - discretization , mathematics , convergence (economics) , numerical analysis , numerical stability , type (biology) , stability (learning theory) , scheme (mathematics) , mathematical analysis , computer science , ecology , machine learning , economics , biology , economic growth

In this paper, a numerical approach is proposed based on the variation-of-constants formula for the numerical discretization Langevin-type equations. Linear and non-linear cases are treated separately. The proofs of convergence have been provided for the linear case, and the numerical implementation has been executed for the non-linear case. The order one convergence for the numerical scheme has been shown both theoretically and numerically. The stability of the numerical scheme has been shown numerically and depicted graphically.

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