کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4634146 | 1340687 | 2008 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Improved generalized quasilinearization method and rapid convergence for reaction diffusion equations
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
In the method of quasilinearization or the method of generalized quasilinearization we assume that âkf(t,x,u)âuk exists, where f(t,x,u) is the forcing function and obtain kth order of convergence. In this paper, we assume a weaker condition namely, âk-1f(t,x,u)âuk-1 exists and Lipschitzian in u and develop generalized quasilinearization method to reaction diffusion equations. The iterates will be different depending on âk-1f(t,x,u)âuk-1 is nondecreasing or nonincreasing in u and k being even or odd. Finally, we prove that the sequences generated by the generalized quasilinearization method converge to the unique solution of the nonlinear reaction diffusion equation and the convergence is of order k.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 203, Issue 2, 15 September 2008, Pages 563-572
Journal: Applied Mathematics and Computation - Volume 203, Issue 2, 15 September 2008, Pages 563-572
نویسندگان
Tanya G. Melton, A.S. Vatsala,