12.5 points Differential Equation Estimate the second derivative of the following function using stencils for the FORWARD an derivatives for an order of accuracy of O(h2) for each. Use a step size of h - 1. f(x)-x-2x2+x6 d CENTRAL ro-22.) Second derivative, Forward Difference Approximation, O(h2)- Second derivative, Central Difference Approximation, O(h2)- Which of the two methods is closer to the true value? (Forward/Central)
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Estimate the second derivative of the following function using stencils for the FORWARD and CENTRAL derivatives for an order of accuracy of O(h2) for each. Use a step size of h -1. fo)x-2x2...
Compute forward and backward difference approxi- aion 21.1 ns of O(h) and Oh), and central difference approxi- mations of 0(h2) and O(h) for the first derivative of y sin x at π/ 12. Estimate the...
Compute forward and backward difference approxi- aion 21.1 ns of O(h) and Oh), and central difference approxi- mations of 0(h2) and O(h) for the first derivative of y sin x at π/ 12. Estimate the true percent 4 using a value of x=π/ relative error ε, for each approximation.
Compute forward and backward difference approxi- aion 21.1 ns of O(h) and Oh), and central difference approxi- mations of 0(h2) and O(h) for the first derivative of y sin x at...
Use forward and backward difference approximations of O(h)
Use forward and backward difference approximations of O(h) and a centered difference approximation of O(h2) to estimate the first derivative of the following function:f(x)=25x³-6x²+7x-88Evaluate the derivative at x=2 using a step size of h=0.25. Compare your results with the true value of the derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion.
3. Consider the following second-order ODE: Using the central difference formula for approximating the second derivative,...
3. Consider the following second-order ODE: Using the central difference formula for approximating the second derivative, discretize the ODE (rewrite the equation in a form suitable for solution with the finite difference method) a. b. If the step size is h-0.5, what is the value of the diagonal elements in the resulting matrix of coefficients of the system of linear equations that has to be solved?
Chapter 2.02: Problem #3 Using forward divided difference scheme, find the first derivative of the function f(x) - sin(...
Chapter 2.02: Problem #3 Using forward divided difference scheme, find the first derivative of the function f(x) - sin(2x) at - x/3 correct within 3 significant digits. Start with a step size of h 0.01 and keep halving it till you find the answer. ее NOTE #1: The above mentioned problems are taken from the book: Numerical Methods with Applications, 2nd edition, by: A. Kaw& E. E. Kalu
(5) Do all parts (a) Let f be a function, and let >0. Write explicit forsmulas for the second difference and second central difference operators, Δ, and each of which depend on h (b) For a fun...
(5) Do all parts (a) Let f be a function, and let >0. Write explicit forsmulas for the second difference and second central difference operators, Δ, and each of which depend on h (b) For a function u(x, t) of two variables, consider the second order partial differ- ential equation CER This is the so-called snave equation. Construct a numerical method for approx imating solutions to this equation, by using the second forward difference for the variable t, and the...
3. Consider the function f(x) = -0.1.24 – 0.15x3 – 0.522 – 0.25x + 1.2. (a)...
3. Consider the function f(x) = -0.1.24 – 0.15x3 – 0.522 – 0.25x + 1.2. (a) Obtain the analytical expression (i.e. True or Exact Solution) for the first derivative, Eval- uate its value at 1 =0.5. Box your answer and label it as fexact- (b) Now assume the function is discretized on a grid with uniform spacing of h. Evaluate your finite difference approximation at x = 0.5 using central differencing with step sizes starting at 1 and re- duced...
Compute forward and backward difference approxi- aion 21.1 ns of O(h) and Oh), and central difference approxi- mations of 0(h2) and O(h) for the first derivative of y sin x at π/ 12. Estimate the true percent 4 using a value of x=π/ relative error ε, for each approximation.
Compute forward and backward difference approxi- aion 21.1 ns of O(h) and Oh), and central difference approxi- mations of 0(h2) and O(h) for the first derivative of y sin x at...
3. Consider the following second-order ODE: Using the central difference formula for approximating the second derivative, discretize the ODE (rewrite the equation in a form suitable for solution with the finite difference method) a. b. If the step size is h-0.5, what is the value of the diagonal elements in the resulting matrix of coefficients of the system of linear equations that has to be solved?
Chapter 2.02: Problem #3 Using forward divided difference scheme, find the first derivative of the function f(x) - sin(2x) at - x/3 correct within 3 significant digits. Start with a step size of h 0.01 and keep halving it till you find the answer. ее NOTE #1: The above mentioned problems are taken from the book: Numerical Methods with Applications, 2nd edition, by: A. Kaw& E. E. Kalu
(5) Do all parts (a) Let f be a function, and let >0. Write explicit forsmulas for the second difference and second central difference operators, Δ, and each of which depend on h (b) For a function u(x, t) of two variables, consider the second order partial differ- ential equation CER This is the so-called snave equation. Construct a numerical method for approx imating solutions to this equation, by using the second forward difference for the variable t, and the...
3. Consider the function f(x) = -0.1.24 – 0.15x3 – 0.522 – 0.25x + 1.2. (a) Obtain the analytical expression (i.e. True or Exact Solution) for the first derivative, Eval- uate its value at 1 =0.5. Box your answer and label it as fexact- (b) Now assume the function is discretized on a grid with uniform spacing of h. Evaluate your finite difference approximation at x = 0.5 using central differencing with step sizes starting at 1 and re- duced...
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