Question l: Solve the differential equation y yx -.ly for y(0.5) and >(I), where () dy dx (c) Usi...
Question 1 Solve the differential equation i -yx2-1.ly for v(0.5) and y(), where y(0) -1 (a) Analytically. (b) Using Ralston method with h 0.5. (This part is for practice only, no need for dy dx submission) (c) Using Heun's method with h 0.5. Perform 2 corrector iterations per step. (d) Using 4h-order RK method with h0.5 (e) Using Non-Self Starting Heun's method with h 0.5 () Using Adams 2-step method with h 0.5 (This part is for practice only, no...
Question l: Solve the differential equation--=yr-lly for y(0.5) and y(1), where y(0)=1 (a) Analytically (b) Using Ralston method with h 0.5. (This part is for practice only, no need for dy dx submission) (c) Using Heun's method with h 0.5. Perform 2 corrector iterations per step. (d) Using 4th-order RK method with h = 0.5 (e) Using Non-Self Starting Heun's method with h 0.5 (f) Using Adams 2-step method with h 0.5 (This part is for practice only, no need...
(20 pts) 4. Solve the differential equation dy = yt? - 1.17 dt over the time interval of [O, 1.5) with the step size of 0.5 and y(0=1. 1) Obtain the analytical result. 2) Use Euler's method. 3. Use Heun's method with iterating the corrector. Do two iterations in the corrector step.
Question Salethe aiferniad q -Lly far yo.s) md y<(), whee yo)-1. (a) Analytically (b) Using Ralston method with h-0.5. (This part is for practice only, no need for submission) (c) Using Heun's method with h 0.5. Perform 2 corrector iterations per step. (d) Using 4th-order RK method with h-0.5. (e) Using Non-Self Starting Heun's method with h = 0.5 (0 Using Adams 2-step method with h 0.5(This part is for practice only, no need for submission) For parts (e) and...
1. Solve the following initial value problem over the interval from x- 0 to 0.5 with a step size h-0.5 where y(0)-1 dy dx Using Heun method with 2 corrector steps. Calculate g for the corrector steps. Using midpoint method a. b. 1. Solve the following initial value problem over the interval from x- 0 to 0.5 with a step size h-0.5 where y(0)-1 dy dx Using Heun method with 2 corrector steps. Calculate g for the corrector steps. Using...
Numerical methods for engineers (30%) ORDINARY DIFFERENTIAL EQUATIONS Solve ODE dy/dx-3xy, where xo-1; yo-2, with step size h-0.1, (calculate only the first point, ie at x,-1.1 yiz?, )using (a) Euler's method (b) Heun's method (b) Fourth-order RK's method 4"
PLEASE PLEASE,ONLY ANSWER THIS QUESTION IF YOU COULD GIVE ME THE MATLAB CODE.THANK YOU. Solve the following ODE from x = 4 to x = 4.5 using a step size of h = 0.5 with non-self-starting Heun Method, where y(3.5) = 0.244898 and y(4) = 0.1875. List the values for the Predictor and the Corrector with three iterations only. Make sure you include 4 decimals in your answer. dy dx 3y + = 0 Example answer: 0.2500 X DO) pl...
For the following differential equation: (x^3)dy/dx+y^4+3=0 where dy/dx is the first derivative of y with respect to x, () means power. The equation has initial values y=2.00 at x=1.00 Using Euler method with a step in the x direction of h=0.30: Show the equation to use to generate values of (2 marks) Calculate the missing values of y in the table below I .1.30 1.00 2.00 1.60 For (2 marks)
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
PROBLEMS 22.1 Solve the following initial value problem over the interval from 0to2 where yo) 1.Display all your results on the same graph. dy=vr2-1.ly dt (a) Analytically. (b) Using Euler's method with h 0.5 and 0.25. (c) Using the midpoint method with h 0.5 (d) Using the fourth-order RK method with h 0.5. PROBLEMS 22.1 Solve the following initial value problem over the interval from 0to2 where yo) 1.Display all your results on the same graph. dy=vr2-1.ly dt (a) Analytically....