Help with these questions please.
Help with these questions please. A mathematical model has been described by an engineer into the following differential equation: dy dx y(0) 2.5 Demonstrate an Euler method simulation of y versus x...
Question 4 A mathematical model has been described by an engineer into the following differential equation: dy 0.5x0 dx y(0) 2.5 Demonstrate an Euler method simulation of y versus x with a tabular algorithm using a. 0.5 and 0.0 3.0. x Demonstrate a 4th-order Runge Kutta method simulation of y versus x with a tabular b. algorithm using дх-0.5 and 0.0 XS 3.0. What can you say about y(x) and the methods used? c. Question 4 A mathematical model has...
The differential equation : dy/dx = 2x -3y , has the initial conditions that y = 2 , at x = 0 Obtain a numerical solution for the differential equation, correct to 6 decimal place , using , The Euler-Cauchy method The Runge-Kutta method in the range x = 0 (0.2) 1.0
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)
3. Consider the differential equation dy 2x2y dx 0, y 1 In the following questions work to 4 decimal places with the initial conditions x = throughout and give your answer to 3 decimal places, or use exact fractions (a) Use the Euler method to calculate an estimate of the value of y after four steps of length h 0.5 [4 marks] (b) Use the Modified Euler method to calculate an estimate of the value of y after two steps...
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...
Given (dy/dx)=(3x^3+6xy^2-x)/(2y) with y=0.707 at x= 0, h=0.1 obtain a solution by the fourth order Runge-Kutta method for a range x=0 to 0.5
Please show steps. Given 3 dy/dx + 2xy^2 = 5x^2 - x + 1, where y(0) = 5 and using a step size of dx = 1, the value of y(1) using Euler's method is most nearly 5.333 1.010 -0.499 17.822 Given 3 dy/dx + 2xy^2 = 5x^2 - x + 1, where y(0) = 5 and using a step size of dx = 1, the value of y(1) using Runge-Kutta 4^th order method is most nearly 5.333 1.010 -0.499...
Please solve this problem by hand calculation. Thanks Consider the following system of two ODES: dx = x-yt dt dy = t+ y from t=0 to t = 1.2 with x(0) = 1, and y(0) = 1 dt (a) Solve with Euler's explicit method using h = 0.4 (b) Solve with the classical fourth-order Runge-Kutta method using h = 0.4. The a solution of the system is x = 4et- 12et- t2 - 3t - 3, y= 2et- t-1. In...
Using the Runge-Kutta fourth-order method, obtain a solution to dx/dt=f(t,x,y)=xy^3+t^2; dy/dt=g(t,x,y)=ty+x^3 for t= 0 to t= 1 second. The initial conditions are given as x(0)=0, y(0) =1. Use a time increment of 0.2 seconds. Do hand calculations for t = 0.2 sec only.
Runge-Kutta method R-K method is given by the following algorithm. Yo = y(xo) = given. k1-f(xy) k4-f(xi +h,yi + k3) 6 For i = 0, 1, 2, , n, where h = (b-a)/n. Consider the same IVP given in problem 2 and answer the following a) Write a MATLAB script file to find y(2) using h = 0.1 and call the file odeRK 19.m b) Generate the following table now using both ode Euler and odeRK19 only for h -0.01....