In this paper we study the convergence of explicit and implicit finite difference scheme for the first initial‐boundary value problem for one dimensional quasilinear heat‐conduction equation with “unbounded nonlinearity”.
Santrauka. Nagrinėjami vienmates netiesinės šilumos laidumo lygties skaitiniai sprendimo metodai, kai lygtis turi tik silpnąjį sprendinį. Lygties koeficientai yra stipriai netiesiniai. Ištirtos išreikštinė ir neišreikštinė baigtinių skirtumų schemos. Aproksimuojant funkcijas panaudoti Steklovo vidurkinimo operatoriai. Gautieji paklaidų įverčiai yra suderinti su diferencialinio uždavinio sprendinio glodumu.
Jovanović, B. S., Matus, P. P., & Shchehlik, V. S. (2000). The estimates of accuracy of difference schemes for the nonlinear heat equation with weak solution. Mathematical Modelling and Analysis, 5(1), 86-96. https://doi.org/10.3846/13926292.2000.9637131
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