By Robert L. Borrelli
Книга Differential Equations: A Modeling viewpoint Differential Equations: A Modeling viewpoint Книги Математика Автор: Robert L. Borrelli, Courtney S. Coleman Год издания: 2004 Формат: djvu Издат.:Wiley Страниц: 736 Размер: 28,3 Mb ISBN: 0471433322 Язык: Английский0 (голосов: zero) Оценка:This potent and sensible new version maintains to target differential equations as a robust device in developing mathematical types for the actual global. It emphasizes modeling and visualization of options all through. every one bankruptcy introduces a version after which is going directly to examine recommendations of the differential equations concerned utilizing an built-in analytical, numerical, and qualitative technique. The authors current the fabric in a fashion that is transparent and comprehensible to scholars in any respect degrees. through the textual content the authors express their enthusiasm and pleasure for the examine of ODEs.
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Extra resources for Differential Equations: A Modeling Perspective
This is rarely acceptable. Your best option is to find a computer with more memory. Modern computer architectures have complex memory hierarchies. The registers in the CPU are the fastest, so you do best if you can keep data in registers as long as possible. Below the registers can be several layers of cache memory. Below the cache is RAM, and below that is disk. Cache memory is faster than RAM, but much more expensive, so a cache is small. Simple things such as ordering loops to improve the locality of reference can speed up a code dramatically.
7. Use tight tolerances, Newton's method, and a tridiagonal Jacobian. y. d-6]; parms=[40, 1, 0, 1, 1, 1]; uhist=zeros(nx+2,nt); uold=zeros(nx,1); for it=l:nt-l [unew, it_hist, ierr] =nsold (uold,' f time', tol, parms) ; uhist(2:nx+1,it+1)=unew; uold=unew; end 7, 7. Plot the results. 7. 4. 13). 50 Chapter 2. Finding the Newton Step with Gaussian Elimination You can see from the plot that u(x, t) tends to a limit as t —> oo. 14) would be to solve the time-dependent problem and look for convergence of u as t —> oo.
Use tight tolerances, Newton's method, and a tridiagonal Jacobian. y. d-6]; parms=[40, 1, 0, 1, 1, 1]; uhist=zeros(nx+2,nt); uold=zeros(nx,1); for it=l:nt-l [unew, it_hist, ierr] =nsold (uold,' f time', tol, parms) ; uhist(2:nx+1,it+1)=unew; uold=unew; end 7, 7. Plot the results. 7. 4. 13). 50 Chapter 2. Finding the Newton Step with Gaussian Elimination You can see from the plot that u(x, t) tends to a limit as t —> oo. 14) would be to solve the time-dependent problem and look for convergence of u as t —> oo.