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by: Nick Rowe

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Numerical Methods For Partial Differential Equations I CS 61500

Marketplace > Purdue University > ComputerScienence > CS 61500 > Numerical Methods For Partial Differential Equations I
Nick Rowe
Purdue
GPA 3.68

Staff

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This 2 page Class Notes was uploaded by Nick Rowe on Saturday September 19, 2015. The Class Notes belongs to CS 61500 at Purdue University taught by Staff in Fall. Since its upload, it has received 65 views. For similar materials see /class/208080/cs-61500-purdue-university in ComputerScienence at Purdue University.

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Date Created: 09/19/15
0de45 Differential Equation Solver This routine uses a variable step Runge Kutta Method to solve differential equations numerically The syntax for 0de45 for rst order differential equations and that for second order differential equations are basically the same However the m les are quite different 7 I First Order Equations y T folly 050 yo A Create a m le for fty see the tutorial on numerical methods and m les on how to do this Save le as for example ypm B Basic syntax for 0de45 At a MATLAB prompt type tyode45 yp t0tf yO your version of 0de45 may not require brackets around to tf yp the 111 file of the function fty saved as ypm t0 tf initial and terminal values of t y0 initial value of y at to tgy y3t C For example to numerically solve ya 7 72 over the interval 1 S t S 4 l o Create and save the le ypm for the function It y 315 9 At a MATLAB prompt type tylode45 yp 14 2 your version of 0de45 may not require backets around 14 9 To print results type ty c To plot results type plot ty 0 To plot results type with a 77 symbol plot ty y 2005 y 105 y 905 H Second Order Equations yt0 yo 7 750 Q1 A First convert 2nd order equation above to an equivalent system of 1 order equations Let 01 y 02 y 50392 7wherext 75515 lxgeqlttgtxpplttgtx2gltt 10 90 20 w B Create and save a m le which will return a vector valued function This is a little tricky so here is a speci c example Suppose the system is as below and 0 S t S 4 Illg 7 7 95 715051 63th 3sin2t 7Where 5610 7 27 5620 7 839 o Create the following function le and save it as Fm function xpFtx xpzeros21 quotA since output must be a column vector xp1x2 xp2 tx1exptx23sin2t quotA don t forget after each line 9 Basic syntax for 0de45 At MATLAB prompt7 type txode45 F t0tf x10x20 F the 111 file of the vector function saved as above t0 tf initial and terminal values of 15 x10 initial value of 01 at to x10a 1t0 x20 initial value of 02 at to x20a 2t0 The example above becomes tx ode45 F 04 2 8 9 Since x105 y to print out the values of the solution y for to S t S 15f type t x 1 To plot the solution on a graph 15 vs y type plot tx 1 This is because the vector x has 13 component 01 y and 2 component 02 y c To plot 01 vs 02 phase plane type plot x 1 x 2

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