کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4641460 | 1341309 | 2008 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Hermite-Birkhoff-Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
A four-stage Hermite-Birkhoff-Obrechkoff method of order 14 with four quantized variable steps, denoted by HBOQ(14)4, is constructed for solving non-stiff systems of first-order differential equations of the form yâ²=f(t,y) with initial conditions y(t0)=y0. Its formula uses yâ², yâ³ and yâ´ as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads to multistep- and Runge-Kutta-type order conditions which are reorganized into linear Vandermonde-type systems. To reduce overhead, simple formulae are derived only once to obtain the values of Hermite-Birkhoff interpolation polynomials in terms of Lagrange basis functions for 16 quantized step size ratios. The step size is controlled by a local error estimator. When programmed in C ++, HBOQ(14)4 is superior to the Dormand-Prince Runge-Kutta pair DP(8,7)13M of order 8 in solving several problems often used to test higher order ODE solvers at stringent tolerances. When programmed in Matlab, it is superior to ode113 in solving costly problems, on the basis of the number of steps, CPU time, and maximum global error. The code is available on the URL www.site.uottawa.ca/~remi.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 222, Issue 2, 15 December 2008, Pages 608-621
Journal: Journal of Computational and Applied Mathematics - Volume 222, Issue 2, 15 December 2008, Pages 608-621
نویسندگان
Truong Nguyen-Ba, Philip W. Sharp, Rémi Vaillancourt,