Integrate the following values of y from x = 0 to x = 130 using (a)...

Integrate the following values of y from x = 0 to x = 130 using (a) The midpoint rule using intervals of [0 10], [10 30], [30 70], and [70 130] (b) The trapezoid rule using the same intervals (c) Simpson’s rule using the same intervals

x y

0 6

5 12

10 18

20 30

30 42

50 36

70 24

100 18

130 6

Integrate the differential equation dydt = y from t = 0 to t = 1 in one step (i.e., with a t of 1) using the Euler method, the Improved Euler method, and the classical Runge-Kutta method, which is the analog of Simpson’s rule. Assume that the initial value of y is 1. Compare your answers to the correct answer, which is exp(1) = 2.7183. You can do all the calculations with an excel spread sheet. Alternatively, you can do all the calculations by hand.

Expert Solution

By dividing the interval and using formula for each method we can find the result.

orchestra answered 2 years ago

17. Integrate the function sin(x) from 0 to π using Riemann and Simpson integration methods with...

17. Integrate the function sin(x) from 0 to π using Riemann and Simpson integration methods with N subintervals, where N increases by factors of 2 from 2 to 256 (i.e. N = 2, N = 4, etc.). Plot the relative error ∆I/I = [| estimated value - true value |/(true value)], assuming the highest value of N gives the ‘true’ value. Which method converges the fastest?

Solve the IVP using Laplace transforms x' + y'=e^t -x''+3x' +y =0 x(0)=0, x'(0)=1, y(0)=0

Integrate the following function by using symbolic operation in MATLAB. y = x^3 − 2x^2 +...

Integrate the following function by using symbolic operation in MATLAB. y = x^3 − 2x^2 + 7

Integrate the following differential equations: a.) y(2x−y+2)dx+2(x−y)dy = 0; b.) yV-2yIV+3y''' - 2y'' = -x + ex.

Solve the system below having the initial values x(0) = 1 = y(0) x’ = x...

Solve the system below having the initial values x(0) = 1 = y(0) x’ = x + 2y y’ = -5x + 3y Please use solving systems of linear des by elimination. Thank You

y′ -xe^x = 0 , y(0) = 4 using laplace transforms

Consider the following first-order ODE dy/dx=x^2/y from x = 0 to x = 2.4 with y(0)...

Consider the following first-order ODE dy/dx=x^2/y from x = 0 to x = 2.4 with y(0) = 2. (a) solving with Euler’s explicit method using h = 0.6 (b) solving with midpoint method using h = 0.6 (c) solving with classical fourth-order Runge-Kutta method using h = 0.6. Plot the x-y curve according to your solution for both (a) and (b).

Solve the following differential equations: 1.) y"(x)+ y(x)=4e^x ; y(0)=0, y'(0)=0 2.) x"(t)+3x'(t)+2x(t)=4t^2 ; x(0)=0, x'(0)=0

Using the change of variables u=x^2y and v=y/x, integrate f(x,y) =x^2y^2 over the region bordered by...

Using the change of variables u=x^2y and v=y/x, integrate f(x,y) =x^2y^2 over the region bordered by y= 1/x^2,y= 3/x^2, y=x and y= 2x.

Find y as a function of x if y′′′+25y′=0 y(0)=2, y′(0)=20, y′′(0)=−100 y(x)=

Question