Abstract
In this paper we construct the finite-difference scheme for the singularly perturbed boundary value problem for the fourth-order elliptic differential equation on the basis of paper [1], and prove the uniform convergence of this scheme with respect to the small parameter ε in the discrete energy norm. Finally, we give a numerical example.
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References
Su Yu-cheng and Liu Guo-qing, Asymptotic solution of singular perturbation problems for the fourth-order elliptic differential equations,Appl. Math. and Mech.,11, 7 (1990), 637–650.
Comstock, C., Singular perturbations of elliptic equations I,SIAM J. Appl. Math.,20 (1971), 491.
Ladyzhenskaya, O. A,The Boundary Problems of Mathematical Physics, Springer-Verlag (1985).
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Yu-cheng, S., Guo-qing, L. Numerical solution of singular perturbation problems for the fourth-order elliptic differential equations. Appl Math Mech 12, 943–966 (1991). https://doi.org/10.1007/BF02451481
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DOI: https://doi.org/10.1007/BF02451481