Solve equations using the fourth order runge-kutta method

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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

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