Question
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Consider the system of ordinary differential equations where Xi are the concentration of species in a chemical reaction and k's are the rate constants. The rate constants are given by k1 = .13 times 10-10, k2 = .39 times 10-11, k3 = .14 times 10-12, k1 = .4 times 10-10. The initial concentrations are given by x1(0) = 1. times 10+11, x2(0) = 1. times 10+11, x3(0) = x4(0) = x5(0) = x6(0) = 0. [RK = Runge-Kutta] Use two different methods to intergate the equations forward untill the reaction is complete (x = 0). Use the RK-Fehlberg and use a lower order RK method. Study the accuracy of the schemes at equilibrium. How close is it to zero, (i.e, x = 0 or f(x) = 0 at final time.) Plot the time history of the concentrations as a function of time.
Explanation / Answer
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