Abstract
A numerical method for singularly perturbed quasilinear boundary value problems without turning points is proposed: the continuous problem is transformed by introducing a special new independent variable and then finite-difference schemes are applied. The first order convergence uniform in the perturbation parameter is proved in the discreteL 1-norm. The numerical results show the pointwise convergence, too.
Zusammenfassung
Ein numerisches Verfahren für quasilineare, singulär gestörte Randwertaufgaben ohne Umkehrpunkte wird angegeben: das kontinuierliche Problem wird durch spezielle neue unabhängige Variable transformiert und danach werden Differenzenverfahren verwendet. Die Konvergenz erster Ordnung gleichmäßig bezüglich des Störungsparameters wird in der diskretenL 1-Norm bewiesen. Die numerischen Ergebnisse zeigen auch punktweise Konvergenz.
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Vulanović, R. A uniform numerical method for quasilinear singular perturbation problems without turning points. Computing 41, 97–106 (1989). https://doi.org/10.1007/BF02238732
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DOI: https://doi.org/10.1007/BF02238732