4th order runge kutta method

\fSelect all strategies that you can use to improve the solution of a first order ordinary differential equation, starting from a base case of Euler's method: Use fourth order Runge Kutta method Use Heun's method Use second order Runge Kutta method O Increase the step size Use first order Runge Kutta method O Decrease the step sizeConsider a birth and death process X(t), t 2 0, such as the branching process, that has state space {0, 1, 2, ...} and birth and death rates of the form Ax = x1 and Hx = XH, x 2 0, where 1 and u are nonnegative constants. Set my(t) = E.(X(t)) = > yP x,(t). )=0 (a) Write the forward equation for the process. (b) Use the forward equation to show that my(t) = (2 - u)m.(t). (c) Conclude that my(t) = xe(2-4)tWrite down the iterative schemes for the Jacobi, Gauss-Seidel and SOR methods. Explain how SOR is obtained from the Gauss-Seidel method. Explore convergence property of the Jacobi and SOR method for the system A,r = b 0 0 .. . 0 b = [1... 17 n = 30 0 2 Use r() = [000.. . Of , Wapt = 1+ sin Iterate until (x - z()| $ 0.00005 The exact solution a can be found as r = A\\b Implement the SOR method (.m file should be submitted). Jacobi and Gauss-Seidel can be found on the webpage (code Create a table k Error Jacobi Error SOR Ratio Jacobi (c) Ratio SOR (c) E. EsOR 10 K where E Janda 5law- error estimate for Jacobi, Egon - error estimate for SOR, K number of iterations which SOR method needed to reach the prescribed accuracy.2 1. Let A = 3 (a) Compute the spectral radius of A. (b) For the linear system of equations Ax = b where b = , define the Jacobi method. (c) Find out whether the Jacobi method converges for any initial guess To