MATH 417 Numerical Analysis Programming assignment #5 Runge-Kutta-Fehlberg method (with error control) Due, March 7, 2019 Write a program for solving Cauchy problem for a single differential equation of first order applying one of the methods that automatically controls the error less than e by selecting appropriate step-size. Use embedded Runge-Kutta methods either(1) Runge-Kutta-Fehlberg or (2) Euler and modified Euler methods (see Numerical Analysis of Burden and Faires, Ninth Edition, pp. 296-298, or Sixth Edition, pp. 286-292) Specifications (1) To debug and test the work of your program, you may solve the IVP: y'-te y for t E (0,1) and y(0)-0 with exact solution y(t)-\e". (2) Run the program for two values of TOL: 102 and 104 (3) Report the number of steps and the obtained solution at the end point. Plot the obtained approxi- mate solution in the whole interval Computational examples - solve the following problems: (1) In a circuit impressed, voltage E, and resistance R, inductance L, capacitance C in parallel, the current satisfies the differential equation Suppose C-0.3 farad, R 1.4 ohms, L1.7 henries, and the voltage is given by E(t) e_0.0rtsin(2t-r). If i(0)-0, find the current i(t) for 0