کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4628978 1340572 2013 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Control of error in the homotopy analysis of nonlinear Klein–Gordon initial value problems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Control of error in the homotopy analysis of nonlinear Klein–Gordon initial value problems
چکیده انگلیسی

In the present paper, we discuss the application of homotopy analysis to general nonlinear Klein–Gordon type equations. We first outline the method for general forms of the nonlinearity, as well as for general functional forms of the initial conditions. In particular, we discuss a method of controlling the residual error in approximate solutions which may be found via homotopy analysis, through adequate selection of the convergence control parameter. With the general problem outlined, we apply the method to various equations, including the quasilinear cubic Klein–Gordon equation, the modified Liouville equation, the sinh-Gordon equation, and the tanh-Gordon equation. For each of these equations and related initial data, we obtain residual error minimizing solutions which demonstrate the qualitative behavior of the true solutions in each case.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 219, Issue 12, 15 February 2013, Pages 6494–6509
نویسندگان
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