1-) Consider the following first-order model of pollutant uptake: V dx/dt =W-Qx where V = 106,...

   

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1-) Consider the following first-order model of pollutant uptake: V dx/dt =W-Qx where V = 106, W = 106 and Q = 105. Consider a lake with no pollutant initially (i.e., x (0) =0). a) Solve the differential equation for x(t) analytically (the true solution). b) Use Euler's method with the step size h = 0.2 to obtain value of x at time, t, equals 10. Compute the error between Euler's solution and true solution. Repeat the analysis with h = 0.1 and 0.05. Comment on the results. What is the order of accuracy for this method? c) Repeat the process and analysis explained in part (b) with the fourth-order Runge-Kutta (RK4) method. Activate Windows 1-) Consider the following first-order model of pollutant uptake: V dx/dt =W-Qx where V = 106, W = 106 and Q = 105. Consider a lake with no pollutant initially (i.e., x (0) =0). a) Solve the differential equation for x(t) analytically (the true solution). b) Use Euler's method with the step size h = 0.2 to obtain value of x at time, t, equals 10. Compute the error between Euler's solution and true solution. Repeat the analysis with h = 0.1 and 0.05. Comment on the results. What is the order of accuracy for this method? c) Repeat the process and analysis explained in part (b) with the fourth-order Runge-Kutta (RK4) method. Activate Windows