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1. Use the method of undetermined coefficients to compute the coefficients of a finite difference approximation...
answer is shown in bold, please show steps to get answer <13 > Use the method of undetermined coefficients to derive an approximation for the second derivative of the following form and fin...
answer is shown in bold, please show steps to get answer
<13 > Use the method of undetermined coefficients to derive an approximation for the second derivative of the following form and find the error f"(x) A=C Af(x-h) +Bf(x) +cf(x+h)
Use the method of undetermined coefficients to derive an approximation for the second derivative of the following form and find the error f"(x) A=C Af(x-h) +Bf(x) +cf(x+h)
3. A five-point centered finite difference approximation to the first derivative is given by - f...
3. A five-point centered finite difference approximation to the first derivative is given by - f (x + 2h) +8f (x + h) – 8f (x – h) + f(x – 2h) 12h (a) What is the error term associated with this formula? (b) Numerically verify the order of approximation using f(x) = (1 + x2)-1 at x = 1 using the values h = 0.1, 0.01, 0.001.
Question 1 15 Points) It is always desirable to have/ use the finite difference approximation wit...
Question 1 15 Points) It is always desirable to have/ use the finite difference approximation with error term. Please using the Taylor Series: higher order of truncation sw(x) h" +R 2! 3! (I) Derive the following forward difference approximation of the 2nd orde 2) What is the order of error for this case? derivative of f(x). f" derivative off(x) h2
Question 1 15 Points) It is always desirable to have/ use the finite difference approximation with error term. Please using...
6 (In this problem, three decimal place approximations suffice.) Use a finite difference approximation, with a...
6 (In this problem, three decimal place approximations suffice.) Use a finite difference approximation, with a uniform mesh of step size h = j, to find an approximate solution of Poisson's equation vu €214 on the unit square (0, 1] x [0,1] with boundary conditions: u(x,0) = x3, u(x,1) = cos(rx + ), (0, y) = -4°, u(1, y) = (1 - 2y)? Then u(3, 3) = A -0.512 B -0.256 C 0.016 D 0.064 E 0.128.
Objective: Solve the wave equation numerically using finite difference methods with both dirichle...
Need help solving it using matlab with for loop
Objective: Solve the wave equation numerically using finite difference methods with both dirichlet and neumann conditions. Consider the wave equation for a string with fixed ends, L=1. lu lu Initial conditions. To make the string behave like a plucked guitar string, use a triangual initial condition. For x less than or equal to 0.5, set u(x, t 0) = 2HX and for x greater than 0.5, use u(x, t = 0)...
ME/AE 342 - Numerical Methods in Engineering with Applications Homework 2 1. Use finite difference approximation...
ME/AE 342 - Numerical Methods in Engineering with Applications Homework 2 1. Use finite difference approximation to compute f'(2.36), /'(2.37) and /"(2.37) from the data 2.36 2.37 2.38 2 .39 0.85866 0.86289 0.86710 0.87129 1() 2. Estimate f'(1) from the following data using either forward or backward dif- ference 1 f(0) 0 .97 0.85040 1.00 1.05 0.84147 0.82612 3. Use polynomial interpolation to compute f' and l" at r = 0, using the data be- low. Hint: Find the Lagrange...
11. In an introductory calculus course, you may have seen of the form approximation formulas for...
11. In an introductory calculus course, you may have seen of the form approximation formulas for integrals f(t)dt wf(a,), 2 where the a, are equally spaced points on the interval (a,b) and the u, are certain "weights (giving Riemann sums, trapezoidal sums, or showed that, with the same computational effort (same type of formula) we can get better approximations if we don't require the a, to be equally spaced. Simpson's rule depending on their values). Gauss Consider the space P,...
There are also approximations of higher order derivatives that can be computed using only values ...
Number 9 requires number 8 so please can you answer
both? Thanks. Here's more context:
There are also approximations of higher order derivatives that can be computed using only values of the original function. Consider the approximation: u(a + 2h)-2u(a + h) + u (a) h2 8. Using your knowledge of Taylor series, what derivative is approximated by Equa Many different combinations of terms can be used to create approximations to deriva- tion??? What is the order of the approximation?...
. (25 points) The recurrence relation for the Newton's Raphson method is a)0.1.2 f(r.) F(z.) The ...
. (25 points) The recurrence relation for the Newton's Raphson method is a)0.1.2 f(r.) F(z.) The derivative of the function can be approximately evaluated using finite-difference method. Consider the Forward and Centered finite-difference formulas Forward Finite-Difference Centered Finite-Difference 2h It is worthwhile to mention that modified secant method was derived based on the forward finite- difference formula. Develop a MATLAB functions that has the following syntax function [root,fx,ea,iter]-modnetraph (func,x0,h,es,maxit,sethod, varargin) % modnevtraph: root location zeroes of nonlinear equation f (x)...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr whic...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
answer is shown in bold, please show steps to get answer
<13 > Use the method of undetermined coefficients to derive an approximation for the second derivative of the following form and find the error f"(x) A=C Af(x-h) +Bf(x) +cf(x+h)
Use the method of undetermined coefficients to derive an approximation for the second derivative of the following form and find the error f"(x) A=C Af(x-h) +Bf(x) +cf(x+h)
3. A five-point centered finite difference approximation to the first derivative is given by - f (x + 2h) +8f (x + h) – 8f (x – h) + f(x – 2h) 12h (a) What is the error term associated with this formula? (b) Numerically verify the order of approximation using f(x) = (1 + x2)-1 at x = 1 using the values h = 0.1, 0.01, 0.001.
Question 1 15 Points) It is always desirable to have/ use the finite difference approximation with error term. Please using the Taylor Series: higher order of truncation sw(x) h" +R 2! 3! (I) Derive the following forward difference approximation of the 2nd orde 2) What is the order of error for this case? derivative of f(x). f" derivative off(x) h2
Question 1 15 Points) It is always desirable to have/ use the finite difference approximation with error term. Please using...
6 (In this problem, three decimal place approximations suffice.) Use a finite difference approximation, with a uniform mesh of step size h = j, to find an approximate solution of Poisson's equation vu €214 on the unit square (0, 1] x [0,1] with boundary conditions: u(x,0) = x3, u(x,1) = cos(rx + ), (0, y) = -4°, u(1, y) = (1 - 2y)? Then u(3, 3) = A -0.512 B -0.256 C 0.016 D 0.064 E 0.128.
Need help solving it using matlab with for loop
Objective: Solve the wave equation numerically using finite difference methods with both dirichlet and neumann conditions. Consider the wave equation for a string with fixed ends, L=1. lu lu Initial conditions. To make the string behave like a plucked guitar string, use a triangual initial condition. For x less than or equal to 0.5, set u(x, t 0) = 2HX and for x greater than 0.5, use u(x, t = 0)...
ME/AE 342 - Numerical Methods in Engineering with Applications Homework 2 1. Use finite difference approximation to compute f'(2.36), /'(2.37) and /"(2.37) from the data 2.36 2.37 2.38 2 .39 0.85866 0.86289 0.86710 0.87129 1() 2. Estimate f'(1) from the following data using either forward or backward dif- ference 1 f(0) 0 .97 0.85040 1.00 1.05 0.84147 0.82612 3. Use polynomial interpolation to compute f' and l" at r = 0, using the data be- low. Hint: Find the Lagrange...
11. In an introductory calculus course, you may have seen of the form approximation formulas for integrals f(t)dt wf(a,), 2 where the a, are equally spaced points on the interval (a,b) and the u, are certain "weights (giving Riemann sums, trapezoidal sums, or showed that, with the same computational effort (same type of formula) we can get better approximations if we don't require the a, to be equally spaced. Simpson's rule depending on their values). Gauss Consider the space P,...
Number 9 requires number 8 so please can you answer
both? Thanks. Here's more context:
There are also approximations of higher order derivatives that can be computed using only values of the original function. Consider the approximation: u(a + 2h)-2u(a + h) + u (a) h2 8. Using your knowledge of Taylor series, what derivative is approximated by Equa Many different combinations of terms can be used to create approximations to deriva- tion??? What is the order of the approximation?...
. (25 points) The recurrence relation for the Newton's Raphson method is a)0.1.2 f(r.) F(z.) The derivative of the function can be approximately evaluated using finite-difference method. Consider the Forward and Centered finite-difference formulas Forward Finite-Difference Centered Finite-Difference 2h It is worthwhile to mention that modified secant method was derived based on the forward finite- difference formula. Develop a MATLAB functions that has the following syntax function [root,fx,ea,iter]-modnetraph (func,x0,h,es,maxit,sethod, varargin) % modnevtraph: root location zeroes of nonlinear equation f (x)...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
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