Solve equations using the fourth order runge-kutta method

Reference no: EM131020717

Consider the following second order differential equation

d²y/dx² + ady/dx + by = c

With the initial conditions

y(1) = k1, (dy/dx)_x=1 = k₂

Reduce the second order differential equation to a system of first order differential equations and solve the equations using the FOURTH ORDER Runge-Kutta method for simultaneous equations, to evaluate y(1.2) taking h=0.2 and 0.1, using the following marked data:

a =	40	50	60	70	80	90	100	110	120	125
b=	6	7	8	9	10	11	12	13	14	15
c =	3	9	11	13	15	20	25	30	40
k1=	2	4	6	8	10	12	14	18	20
k2=	1.5	-1,5	2.5	-2.5	3.5	3.5	4.5	4.5

• Use MATHEMATICA to improve accuracy of your results taking h=0.05, 0.025 and 0.0125. Attach your Mathematica sheet with your worked solution sheets.

• Specify the accuracy of your calculations in significant figures. All steps in your calculations must be shown in complete detail.

Reference no: EM131020717

Questions Cloud

Ddisability and the necessary adjustments : You create a research paper on a client with a disability and the necessary adjustments needed for the client. I have selected Parkinson's disease.

What do they mean by a person long-run self : In an article in the Quarterly Journal of Economics, Ted O'Donoghue and Matthew Rabin make the following observation: "People have self-control problems caused by a tendency to pursue immediate gratification in a way that their ‘long-run selves' ..

Briefly discuss what effect the refinancing cost : She wants to pay off our $114,000 mortgage, but I'm not eager to do that because we refinanced only nine months ago, paying $3,000 in fees and costs." Briefly discuss what effect the $3,000 refinancing cost should have on this couple's investment ..

What is the effect of the price ceiling on the market : Redraw the graph illustrating an effective price ceiling, P1. Describe what must be true for this price ceiling to be effective. With an effective price ceiling, which side of the market is the short side? What is the effect of the price ceiling o..

Solve equations using the fourth order runge-kutta method : Reduce the second order differential equation to a system of first order differential equations and solve the equations using the FOURTH ORDER Runge-Kutta method for simultaneous equations

Globalisation of production : With reference to relevant literature, critically discuss how the Chinese SOE, Baosteel, has benefited from both the globalisation of marketsas well as the globalisation of production.

Will the price you paid for the car be one of those factors : After owning a used car for two years, you start having problems with it. You take it to the shop, and a mechanic tells you that repairs will cost $4,000. What factors will you take into account in deciding whether to have the repairs done or to j..

Explain the relationship between the dutch successes : How has the Dutch historical technological relationship with water impacted their ability to address the modern challenge of global sea level rise?

Pay out a liquidating dividend : JJ Industries will pay a regular dividend of $0.75 per share for each of the next four years. At the end of four years, the company will also pay out a liquidating dividend. If the discount rate is 12 percent, and the current share price is $75, what..

User Account

All Pages