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Question 4 Consider the initial value problem Y = 1+(t- y) with y(2) = 1 and...
3. Consider the initial value problem y(t) = y, y(0) = 1. a. Write down (i.e.,...
3. Consider the initial value problem y(t) = y, y(0) = 1. a. Write down (i.e., write the formula which describes one step, Yn+1 = yn + ...) the second order Taylor method with step size h for this initial value problem. b. Write down the time stepping formula Yn+1 = Yn +... for the modified Euler method 9n+1 := yn + hf(en +3.29 + s(tn, yn)), for this initial value problem. c. What is the difference between the two...
3. Consider the initial value problem y'(t) = y2, y(0) = 1. a. Write down (i.e.,...
3. Consider the initial value problem y'(t) = y2, y(0) = 1. a. Write down (i.e., write the formula which describes one step, Yn+1 = yn + ...) the second order Taylor method with step size h for this initial value problem. b. Write down the time stepping formula Yn+1 = Yn +... for the modified Euler method h Yn+1 := yn + hf(tn + h 2:9 » Yn + 5 f (tnYn)), for this initial value problem. c. What...
9) Using Euler method, solve this with following initial conditions that t = 0 when y = 1, for th...
9) Using Euler method, solve this with following initial conditions that t = 0 when y = 1, for the range t = 0 to t = 1 with intervals of 0.25 dr + 2x2 +1=0.3 dt 1o) Using second order Taylor Series method, solve with following initial conditions to-0, xo-1 and h-0.24 11) x(1)-2 h-0.02 Solve the following system to find x(1.06) using 2nd, and 3rd and 4th order Runge-Kutta (RK2, RK3 and RK4)method +2x 2 +1-0.3 de sx)-cox(x/2)...
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find the first-order correction, y (t),...
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find the first-order correction, y (t), for the initial value problem with є * 0 and є is a small parameter.
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find...
Consider the initial value problem * du -11 + u(0) = 1 at 12 Approximate y(0.4)...
Consider the initial value problem * du -11 + u(0) = 1 at 12 Approximate y(0.4) using Taylor series method of order two and two equal time steps.
Please solve Q 7 & 8 7. 14+6 marks] Consider the initial value problem y_y2, 2,y(1) = 1 y'= 1-t (a) Assuming y(t) is bounded on [1, 2], Show that f(t,v)--satisfies Lipschitz condition with...
Please solve Q 7 & 8
7. 14+6 marks] Consider the initial value problem y_y2, 2,y(1) = 1 y'= 1-t (a) Assuming y(t) is bounded on [1, 2], Show that f(t,v)--satisfies Lipschitz condition with respect to y. (b) Use second order Taylor method with h 0.2 to approximate y(1.2), then use the Runge- Kutta method: to compute an approximation of y(1.4). 8. [4 marks) Assuming that a1, o2 are non negative constants, determine the parameters o and β1 of the...
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 equat...
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...
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h 0.05 Find the value of x(0.4) for the coupled first order differential equations toge...
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h 0.05 Find the value of x(0.4) for the coupled first order differential equations together with initial conditions with step size 0.1: 2. dt t+x 3. dx dt = y, dy dt x(0) = 1.2 and --ty +xt2 + y(o) 0.8
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h...
Exercise 1 Consider the initial-value problem y(t)=1+3940), 25t<3; y(2) = 0. a) Show that the problem...
Exercise 1 Consider the initial-value problem y(t)=1+3940), 25t<3; y(2) = 0. a) Show that the problem has a unique solution. b) Compute (by hand) an approximation of y(3) using the forward Euler method with a step size h = 0.5 (namely perform 2 steps of the method).
1. (Hand problem) Apply Euler's Method with step size h=1/4 to the initial value problem V=t+y,...
1. (Hand problem) Apply Euler's Method with step size h=1/4 to the initial value problem V=t+y, Ostsi. y(0) = 1, (1) and find the global error at t = 1 by comparing with the exact solution y(t) = 2e - t-1.
3. Consider the initial value problem y(t) = y, y(0) = 1. a. Write down (i.e., write the formula which describes one step, Yn+1 = yn + ...) the second order Taylor method with step size h for this initial value problem. b. Write down the time stepping formula Yn+1 = Yn +... for the modified Euler method 9n+1 := yn + hf(en +3.29 + s(tn, yn)), for this initial value problem. c. What is the difference between the two...
3. Consider the initial value problem y'(t) = y2, y(0) = 1. a. Write down (i.e., write the formula which describes one step, Yn+1 = yn + ...) the second order Taylor method with step size h for this initial value problem. b. Write down the time stepping formula Yn+1 = Yn +... for the modified Euler method h Yn+1 := yn + hf(tn + h 2:9 » Yn + 5 f (tnYn)), for this initial value problem. c. What...
9) Using Euler method, solve this with following initial conditions that t = 0 when y = 1, for the range t = 0 to t = 1 with intervals of 0.25 dr + 2x2 +1=0.3 dt 1o) Using second order Taylor Series method, solve with following initial conditions to-0, xo-1 and h-0.24 11) x(1)-2 h-0.02 Solve the following system to find x(1.06) using 2nd, and 3rd and 4th order Runge-Kutta (RK2, RK3 and RK4)method +2x 2 +1-0.3 de sx)-cox(x/2)...
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find the first-order correction, y (t), for the initial value problem with є * 0 and є is a small parameter.
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find...
Consider the initial value problem * du -11 + u(0) = 1 at 12 Approximate y(0.4) using Taylor series method of order two and two equal time steps.
Please solve Q 7 & 8
7. 14+6 marks] Consider the initial value problem y_y2, 2,y(1) = 1 y'= 1-t (a) Assuming y(t) is bounded on [1, 2], Show that f(t,v)--satisfies Lipschitz condition with respect to y. (b) Use second order Taylor method with h 0.2 to approximate y(1.2), then use the Runge- Kutta method: to compute an approximation of y(1.4). 8. [4 marks) Assuming that a1, o2 are non negative constants, determine the parameters o and β1 of the...
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...
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h 0.05 Find the value of x(0.4) for the coupled first order differential equations together with initial conditions with step size 0.1: 2. dt t+x 3. dx dt = y, dy dt x(0) = 1.2 and --ty +xt2 + y(o) 0.8
Find the value of x(0.5) for the initial value problem at = thx(0)=1 using Euler's method with step size h...
Exercise 1 Consider the initial-value problem y(t)=1+3940), 25t<3; y(2) = 0. a) Show that the problem has a unique solution. b) Compute (by hand) an approximation of y(3) using the forward Euler method with a step size h = 0.5 (namely perform 2 steps of the method).
1. (Hand problem) Apply Euler's Method with step size h=1/4 to the initial value problem V=t+y, Ostsi. y(0) = 1, (1) and find the global error at t = 1 by comparing with the exact solution y(t) = 2e - t-1.
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