MEEN 221 Numerical Methods 1. A well-known coupled set of dimensionless differential equations (Lotka-Volterra equations) can be used to predict the population of predators and preys in a jungle. These equations are given below Subject to the initial conditions: y(O) = 0.1 x(0) = 0.2, where x and y are the number of predators and preys respectively; and p, q, r and s are constants whose values can be taken as: p = 1 ; q 0.1 Use Euler forward method to solve the pair of ordinary differential equations (equations 1 and 2) for x and y from t = 0 to t = 10. Use a step size oft = 0.01 . Solve by MATLAB or EXCEL. Deliverables: Derive the discretized equations for equations 1 and 2 using Euler forward Method. Compute the solution for the first 20 time indices and complete the table below Index for time, i 1. 2. 0.2 0.1 20 0.2 3, Determine the solution for the time range t = 0 to t = 10 (time indices 0 to 100). Considering this time range: (i) Plot both x and y versus time on the same plot, and on a second plot (ii) Plot y versus X. 4. From your plot in 3(i), at what time does the number of preys become the same as the number of predators? Note: If you solve by MATLAB, you must include your MATLAB script to thedeliverables