To find the numerical solution of the first order differential equations with the initial condition by using Taylor's series method
You are given the initial value problem Approximate the solution with error less than or equal to...
Consider the initial value problem i. Find approximate value of the solution of the initial value problem at using the Euler method with . ii. Obtain a formula for the local truncation error for the Euler method in terms of t and the exact solution . 2,,2 5 0.1 y = o(t) 2,,2 5 0.1 y = o(t)
0.1 Use a Taylor series to approximate ſ sin (x“)dr with error less than 10-15
0.1 11) Use a Taylor series to approximate ſ sin(x*)dx with error less than 10-15 0 12) Find the surface area of x=t? y = 21 ,03t 34 about the x-axis
uestion 3. (a) 1 mark] Use Euler's method to approximate the solution of the initial-value problem at t 0.1 in a single step. (b) [1 miark] Is the problem well-posed on the domain D {(t,y)10-K 0.1, 0 < y < ool? why?
uestion 3. (a) 1 mark] Use Euler's method to approximate the solution of the initial-value problem at t 0.1 in a single step. (b) [1 miark] Is the problem well-posed on the domain D {(t,y)10-K 0.1, 0
Find approximate values of the solution of the given initial value problem at T=0.1, 0.2, 0.3, and 0.4 using Euler method with h=0.1 y'= 0.5-t+2y ; y(o)=1
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.
Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use the improved Euler's method with tolerance to approximate the solution to this initial value problem at t 1. For a tolerance of e-0.01, use a based on absolute error stopping procedure
Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use the improved Euler's method with tolerance to approximate the solution to this initial value problem at t...
Question 1: Given the initial-value problem 12-21 0 <1 <1, y(0) = 1, 12+10 with exact solution v(t) = 2t +1 t2 + 1 a. Use Euler's method with h = 0.1 to approximate the solution of y b. Calculate the error bound and compare the actual error at each step to the error bound. c. Use the answers generated in part (a) and linear interpolation to approximate the following values of y, and compare them to the actual value...
Use a 2 step Euler's method to approximate y(1.8), of the solution of the initial-value problem y' = 2 + 5x2 + 2y, y(1) = 1. If you use a formula, as part of your work you MUST indicate what formula you are using and what values your variables have. y(1.8)
Use a 2 step Euler's method to approximate y(1.2), of the solution of the initial-value problem y' = 1 – 2x2 – 2y, y(1) = 4. If you use a formula, as part of your work you MUST indicate what formula you are using and what values your variables have. y(1.2) =