Question

Compute the first-order forward, backward, and central difference approximations to estimate the first derivative of y...

Compute the first-order forward, backward, and central difference approximations to estimate the first derivative of y = x3 +4x−15 at x = 0 with h = 0.25. Compare your results with the analytical solution.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h^2 )...
Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h^2 ) to estimate the first and second derivatives of f(x)= 0.4x^5 ‐0.2x^3 +6x^2 ‐13 at x=2 using a step size h=1. Repeat the computation using h values of 0.5, 0.25, and 0.1. Compare your results with the exact derivative value at x=2.
find the derivative of cos x at x=1 by first order forward 2nd order and 4th...
find the derivative of cos x at x=1 by first order forward 2nd order and 4th order central schemes with h=0.01
For a given h, a derivative at a point x0 can be approximated using a forward...
For a given h, a derivative at a point x0 can be approximated using a forward difference, a backward difference, and a central difference: f 0 (x0) ≈ f(x0 + h) − f(x0) h forward difference f 0 (x0) ≈ f(x0) − f(x0 − h) h backward difference f 0 (x0) ≈ f(x0 + h) − f(x0 − h) 2h central difference. Using MATLAB or Octave, Write a script that prompts the user for an h value and an x0...
Derive or prove the three point backward difference approximation of the first derivative, aka Dh--f, of...
Derive or prove the three point backward difference approximation of the first derivative, aka Dh--f, of a function f(x), using either polynomial interpolant method (Newton's or Lagrange's) here is the first derivative approximation: f'(x) = (3* f(x) - 4*f(x-h)+ f(x-2h)) /2h , which is congruent to Dh--f
Consider the linear first order system [16] x′ = x + y (1) y′ =4x−2y. (2)...
Consider the linear first order system [16] x′ = x + y (1) y′ =4x−2y. (2) (a) Determine the equilibria of System (1)-(2) as well as their stability. [6] (b) Compute the general solution of System (1)-(2). [6] (c) Determine the solution of the initial value problem associated with System (1)-(2), with initial condition x(0) = 1, y(0) = 2.
3) If f=f(x, y), derive a forward finite difference approximation of 3rd order accuracy, O(h³), for...
3) If f=f(x, y), derive a forward finite difference approximation of 3rd order accuracy, O(h³), for ∂f/∂x.
a)Program a calculator or computer to use Euler's method to compute y(1), where y(x) is the...
a)Program a calculator or computer to use Euler's method to compute y(1), where y(x) is the solution of the given initial-value problem. (Give all answers to four decimal places.) dy dx + 3x2y = 9x2, y(0) = 4 h = 1     y(1) = h = 0.1     y(1) = h = 0.01     y(1) = h = 0.001     y(1) = (b) Verify that y = 3 + e−x3 is the exact solution of the differential equation. y = 3 + e−x3      ⇒     y'...
1218) y=Ax+Cx^B is the general solution of the first-order homogeneous DEQ: (x-y) dx - 2x dy...
1218) y=Ax+Cx^B is the general solution of the first-order homogeneous DEQ: (x-y) dx - 2x dy = 0. Determine A and B. Also, include a manual solution in your portfolio. ans:2 1220) y=Ax+Dx^B is the particular solution of the first-order homogeneous DEQ: (x-y) = 2xy'. Determine A,B, & D given the boundary conditions: x=7 and y=5. Include a manual solution in your portfolio. ans:3
1. (5pts.) Compute the derivative dy/dx for y = 7√ 9π + x ^5 /6 +...
1. (5pts.) Compute the derivative dy/dx for y = 7√ 9π + x ^5 /6 + 27e^x . 3. (5pts.) Write the equation of the tangent line to the graph of y = 3 + 8 ln x at the point where x = 1. 4. (5pts.) Determine the slope of the tangent line to the curve 2x^3 + y^3 + 2xy = 14 at the point (1, 2). 5. (5pts.) Compute the derivative dw/dz of the function w =...
6. Consider the initial value problem y' = ty^2 + y, y(0) = 0.25, with (exact)...
6. Consider the initial value problem y' = ty^2 + y, y(0) = 0.25, with (exact) solution y(t). (a) Verify that the solution of the initial value problem is y(t) = 1/(3e^(-t) − t + 1) and evaluate y(1) to at least four decimal places. (b) Use Euler’s method to approximate y(1), using a step size of h = 0.5, and evaluate the difference between y(1) and the Euler’s method approximation. (c) Use MATLAB to implement Euler’s method with each...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT