{"id":21862,"date":"2020-11-13T21:04:51","date_gmt":"2020-11-13T13:04:51","guid":{"rendered":"https:\/\/swarma.org\/?p=21862"},"modified":"2020-11-13T21:04:51","modified_gmt":"2020-11-13T13:04:51","slug":"%e7%89%9b%e6%b4%a5%e5%a4%a7%e5%ad%a6%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e6%95%99%e6%9d%90%e5%85%8d%e8%b4%b9%e4%b8%8b%e8%bd%bd","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=21862","title":{"rendered":"\u725b\u6d25\u5927\u5b66\u5e38\u5fae\u5206\u65b9\u7a0b\u6559\u6750\u514d\u8d39\u4e0b\u8f7d"},"content":{"rendered":"
\n
<\/section>\n

\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature<\/em>\u3001Science<\/em>\u7b49\u9876\u520a\u7684\u6700\u65b0\u8bba\u6587\uff0c\u8ffd\u8e2a\u590d\u6742\u7cfb\u7edf\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u8ba1\u7b97\u793e\u4f1a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\u3002\u73b0\u5728\u6b63\u5f0f\u63a8\u51fa\u8ba2\u9605\u529f\u80fd\uff0c\u6bcf\u5468\u901a\u8fc7\u5fae\u4fe1\u670d\u52a1\u53f7\u300c\u96c6\u667a\u6591\u56fe\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0a\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605<\/strong>\u3002<\/span>
<\/p>\n


<\/span><\/p>\n

\u5e38\u5fae\u5206\u65b9\u7a0b\uff08ordinary differential equation\uff0c\u7b80\u79f0ODE\uff09\u662f\u63cf\u8ff0\u52a8\u529b\u7cfb\u7edf\u7684\u5fc5\u5907\u5de5\u5177\uff0c\u4e5f\u662f\u5de5\u7a0b\u3001\u7ecf\u6d4e\u7b49\u7cfb\u7edf\u5efa\u6a21\u7684\u57fa\u7840\u65b9\u6cd5\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4eca\u5929\u5411\u5927\u5bb6\u63a8\u8350\u4e00\u672c\u5e38\u5fae\u5206\u65b9\u7a0b\u7684\u6559\u6750  Exploring ODEs <\/em>\uff0c\u8fd9\u662f\u4e00\u672c343\u9875\u7684\u5c0f\u4e66\uff0c\u51fa\u7248\u4e8e2017\u5e74\uff0c\u9488\u5bf9\u9ad8\u5e74\u7ea7\u672c\u79d1\u751f\u3001\u7814\u7a76\u751f\u548c\u76f8\u5173\u79d1\u7814\u5de5\u7a0b\u4eba\u5458\u3002\u4f5c\u8005\u5f00\u653e\u4e86PDF\u7248\u672c\u7684\u4e66\u7a3f\uff0c\u626b\u7801\u5373\u53ef\u5728\u7ebf\u6d4f\u89c8\u5e76\u4e0b\u8f7d\u3002<\/strong><\/span><\/span><\/section>\n
<\/span><\/section>\n
<\/span><\/section>\n
<\/span><\/section>\n
\u626b\u7801\u4e8c\u7ef4\u7801\u6216\u70b9\u51fb\u6587\u672b\u201c\u9605\u8bfb\u539f\u6587\u201d\u5373\u53ef\u4e0b\u8f7dPDF\u6587\u4ef6<\/span><\/strong><\/span><\/section>\n

<\/span><\/section>\n
\u672c\u4e66\u4f5c\u8005\u6709\u4e09\u4f4d\uff1a
<\/span><\/section>\n

<\/span><\/section>\n
\u7b2c\u4e00\u4f5c\u8005 Nick Trefethen \u662f\u725b\u6d25\u5927\u5b66\u6570\u503c\u5206\u6790\u6559\u6388\uff0c\u6570\u5b66\u7814\u7a76\u6240\u6570\u503c\u5206\u6790\u5c0f\u7ec4\u8d1f\u8d23\u4eba\u3002\u300a<\/span>Numerical Linear Algebra<\/span>\u300b\u662f\u5176\u7ecf\u5178\u6559\u6750\uff0c\u5982\u4eca\u5df2\u66f4\u65b0\u81f3\u7b2c\u4e94\u7248<\/span>\u3002<\/span>\u4ed6\u5728\u6570\u503c\u5206\u6790\u9886\u57df\u6709\u8bb8\u591a\u5f00\u521b\u6027\u8d21\u732e\uff0c\u66fe\u83b7\u5f97\u8bf8\u591a\u8363\u8a89\uff0c\u5e76\u57282020\u5e741\u6708\u83b7\u5f97\u4e86\u7f8e\u56fd\u5de5\u4e1a\u548c\u5e94\u7528\u6570\u5b66\u5b66\u4f1a\u9881\u53d1\u7684\u7ea6\u7ff0\u00b7\u51af\u00b7\u8bfa\u4f9d\u66fc\u5956\u3002Trefethen<\/span>\u5728Google Scholar\u4e0a\u88ab\u5f15\u6b21\u6570\u5df2\u7ecf<\/span>\u8d85\u8fc73\u4e07\u6b21\u3002<\/span><\/section>\n
<\/span><\/section>\n


<\/p>\n

<\/p>\n


<\/section>\n
\u672c\u4e66\u53e6\u5916\u4e24\u4f4d\u4f5c\u8005 <\/span>\u00c1sgeir Birkisson\u66fe\u83b7\u725b\u6d25\u5927\u5b66\u535a\u58eb\u5b66\u4f4d<\/span>\uff0c<\/span>\u540e\u4efb\u804c\u4e8e<\/span>Squarepoint Capital\uff1b<\/span>Tobin A. Driscoll<\/span>\u662f<\/span>\u7279\u62c9\u534e\u5927\u5b66\u6570\u5b66\u7cfb\u6559\u6388\u3002<\/span><\/section>\n

<\/section>\n

<\/span><\/section>\n
\u76ee\u5f55\uff1a
<\/span><\/strong><\/span><\/section>\n

1. Introduction, 1<\/span><\/p>\n

2. First-order scalar linear ODEs, 11 <\/span><\/p>\n

3. First-order scalar nonlinear ODEs, 25 <\/span><\/p>\n

4. Second-order ODEs and damped oscillations, 39 <\/span><\/p>\n

5. Boundary-value problems, 51 <\/span><\/p>\n

6. Eigenvalues of linear BVPs, 63 <\/span><\/p>\n

7. Variable coefficients and adjoints, 77 <\/span><\/p>\n

8. Resonance, 91 <\/span><\/p>\n

9. Second-order equations in the phase plane, 103 <\/span><\/p>\n

1<\/span>0. Systems of equations, 115 <\/span><\/p>\n

11. The fundamental existence theorem, 129 <\/span><\/p>\n

12. Random functions and random ODEs, 141 <\/span><\/p>\n

13. Chaos, 155 <\/span><\/p>\n

14. Linear systems and linearization, 171 <\/span><\/p>\n

15. Stable and unstable fixed points, 185 <\/span><\/p>\n

16. Multiple solutions of nonlinear BVPs, 195 <\/span><\/p>\n

17. Bifurcation, 209 <\/span><\/p>\n

18. Continuation and path-following, 225 <\/span><\/p>\n

19. Periodic ODEs, 237 <\/span><\/p>\n

20. Boundary and interior layers, 253 <\/span><\/p>\n

21. Into the complex plane, 267 <\/span><\/p>\n

22. Time-dependent PDEs, 281 <\/span><\/p>\n

Appendix A: Chebfun and its ODE algorithms, 297 <\/span><\/p>\n

Appendix B: 100 more examples, 309 <\/span><\/p>\n

Index, 329<\/span><\/p>\n


<\/span><\/p>\n

\u4f5c\u8005\u8fd8\u63d0\u4f9b\u4e86\u5206\u7ae0\u8282\u4e0b\u8f7d\u7684\u5730\u5740\uff0c\u5730\u5740\u89c1\uff1a<\/span><\/section>\n
http:\/\/people.maths.ox.ac.uk\/trefethen\/Exploring.pdf<\/span><\/section>\n

<\/p>\n


<\/p>\n

\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/span><\/p>\n