# Write a Matlab script that uses the fourth order Runge-Kutta method…

An Introduction To Matlab Phil RamsdenPhil Ramsden Succor Courseeffect Task Deadline: 25 March 2011 Your courseeffect must inclose a shelter sheet and the aftercited identified pawn that it is your own effect. This attestation signies that this represents my own effect, completed indepen- dently, delayout countenance exclude where acknowledged and uprightly referenced. Signed: Name: CID: Tutorial Group: 1. (20 %) Write a Matlab script that uses the fourth enjoin Runge-Kutta regularity to investigate a numerical disintegration of the dierential equation dx dt = ??t x for 0 t 3, where x(0) = 1. Use a stride bulk of 0:2. Plot your results, delay eligible axis labels and epithet. Compare your acceptances delay the symbolic disintegration: for what appraise of t is the fallacy at its first, and what is its appraise there? What is the appraise of the fallacy at t = 3? Solve frequently delay a stride bulk of 0:1, and frequently nd the fallacy at t = 3. Repeat delay stride bulks of 0:05 and 0:025. The fallacy in the fourth-enjoin Runge-Kutta regularity is reckoned to be fourth enjoin in the stride bulk. What does this balance, and do your results buttress this demand? Give reasons for your acceptance, illustrating delay a diagram if divert. 2. (20 %)Write a Matlab power denominated myodesolver.m that takes as its controversys: • a power discuss f representing the befitting index aspect of a rst-enjoin ODE; • a post vector t representing a set of t-values; • a compute x0 representing an primal appraise of x and returns two post vectors representing the t- and x-coordinates of an ap- instant disintegration. (Note that your rst post vector accomplish merely be the succor controversy, t.) 1 You should use either a succor-enjoin Runge-Kutta regularity or a fourth-enjoin one; reach it manifest which you've separated. Using your solver power, nd a succor- or fourth-enjoin Runge-Kutta disintegration of dx dt = cos(x2 + t) delay x(0) = 0, using a stride bulk of 0:02 and 0 t 6. Show your results in a eligible diagram. 3. (20 %) Write a succor Matlab power denominated myodesolver2.m that takes as its controversys: • a...

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