Newton's first order numerical method.
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This is a homework question. If your against helping students, I understand.
Given the differential equation : dy/dx + 2y = -5, y(0) = 3 Solve using Newton's first order numerical method, taking sufficient steps to estimate y when x = 2.I can't find any examples on how to solve the equation using this method. It would be appreciated if someone showed me how to do this, or pointed me to a useful example. Cheers,Mark Brock Click here to view my blog
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This is a homework question. If your against helping students, I understand.
Given the differential equation : dy/dx + 2y = -5, y(0) = 3 Solve using Newton's first order numerical method, taking sufficient steps to estimate y when x = 2.I can't find any examples on how to solve the equation using this method. It would be appreciated if someone showed me how to do this, or pointed me to a useful example. Cheers,Mark Brock Click here to view my blog
The numerical recipes book(s) has been a God-send for many of us. It was originally for Fortran, then translated to (a rather clunky, but functional) C. The really great thing is that they do a good job of explaining the algorithms. I have, for the most part, just used their explanations and written my own code. Here's a link to their older versions that you can read on-line. http://www.nrbook.com/a/[^] You can also find their most recent versions at www.nr.com The book will explain the Newton method, and have examples of it's use.
David --------- Empirical studies indicate that 20% of the people drink 80% of the beer. With C++ developers, the rule is that 80% of the developers understand at most 20% of the language. It is not the same 20% for different people, so don't count on them to understand each other's code. http://yosefk.com/c++fqa/picture.html#fqa-6.6 ---------
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The numerical recipes book(s) has been a God-send for many of us. It was originally for Fortran, then translated to (a rather clunky, but functional) C. The really great thing is that they do a good job of explaining the algorithms. I have, for the most part, just used their explanations and written my own code. Here's a link to their older versions that you can read on-line. http://www.nrbook.com/a/[^] You can also find their most recent versions at www.nr.com The book will explain the Newton method, and have examples of it's use.
David --------- Empirical studies indicate that 20% of the people drink 80% of the beer. With C++ developers, the rule is that 80% of the developers understand at most 20% of the language. It is not the same 20% for different people, so don't count on them to understand each other's code. http://yosefk.com/c++fqa/picture.html#fqa-6.6 ---------
Thanks! :)
Mark Brock Click here to view my blog
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This is a homework question. If your against helping students, I understand.
Given the differential equation : dy/dx + 2y = -5, y(0) = 3 Solve using Newton's first order numerical method, taking sufficient steps to estimate y when x = 2.I can't find any examples on how to solve the equation using this method. It would be appreciated if someone showed me how to do this, or pointed me to a useful example. Cheers,Mark Brock Click here to view my blog
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MarkBrock wrote:
I can't find any examples on how to solve the equation using this method.
You obviously haven't looked. :doh:
Doing my part to piss off the religious right.
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Sure I have, I read this, searched Google, and found "Code Project Math Forum: Mathematics and Algorithms discussions - Full of people who love to solve differential equations"... ;).
Mark Brock Click here to view my blog
MarkBrock wrote:
searched Google
I searched Google[^] and the material David referenced, albeit in a different location, popped up on the first page. Actually, two different versions of that book. The implementations in the language specific versions of "Numerical Recipes" suck since they're crappy direct, probably machine generated, translations of the original FORTRAN.
Doing my part to piss off the religious right.
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This is a homework question. If your against helping students, I understand.
Given the differential equation : dy/dx + 2y = -5, y(0) = 3 Solve using Newton's first order numerical method, taking sufficient steps to estimate y when x = 2.I can't find any examples on how to solve the equation using this method. It would be appreciated if someone showed me how to do this, or pointed me to a useful example. Cheers,Mark Brock Click here to view my blog
In case anyone cares... I found out that Newton's first order numerical method is actually Euler's method. y(h) = y(0) + h*(dy/dx). It is a way of estimating the solution of a differential equation. Cheers,
Mark Brock Click here to view my blog