NOTE:
• Subject: Numerical Methods for Ordinary Differential Equations: Initial Value Problems.
Homework Answers
Add Answer to:
NOTE:
• Subject: Numerical Methods for Ordinary Differential
Equations: Initial Value Problems.
1. Consider the family...
Question is as follows: NOTE: • Subject: Numerical Methods for Ordinary Differential Equations: Initial Value Problems....
Question is as follows:
NOTE:
• Subject: Numerical Methods for Ordinary Differential
Equations: Initial Value Problems.
______
Useful Information
Implicit Nystrom Method: (aka Milne-Simpson)
Explicit Nystrom Method: (for reference)
Adams-Bashforth Method (AB): (for reference)
Zero-Stability:
Root Condition: (for reference)
3. Consider the 2-step Implicit Nyström Method (aka Simpson's Method): Un+2 – Un = (F(UM) + 4f(Un+1) + f(Un+2)]. (a) Determine the two characteristic polynomials, p() and o(5), for this method. Use these to show that this method is consistent. (b)...
this is numerical analysis. Please do a and b 4. Consider the ordinary differential equation 1'(x)...
this is numerical analysis. Please do a and b
4. Consider the ordinary differential equation 1'(x) = f(x, y(x)), y(ro) = Yo. (1) (a) Use numerical integration to derive the trapezoidal method for the above with uniform step size h. (You don't have to give the truncation error.) (b) Given below is a multistep method for solving (1) (with uniform step size h): bo +1 = 34 – 2n=1 + h (362. Yn) = f(n=1, 4n-1)) What is the truncation...
Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the following initial...
Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = + 1.C: y(0) 0.5 Using Euler's method, and a time step of At = 0.2. do you expect the numerical solution not to oscillate and to be stable? No, because the time step far exceeds the critical value At stable < 0.067 for this problem. None of the above Yes, because Euler's method is explicit and there is...
Numerical Methods for Ordinary Differential Equations: Initial Value Problems 1.10.** Write the IVP x'"' (t) –...
Numerical Methods for Ordinary Differential Equations: Initial
Value Problems
1.10.** Write the IVP x'"' (t) – ax"(t) – bx'(t) – cx = f(t), x(0) = $, s'(0) = n, x"(0) = 5 as a first-order system x'(t) = Ax(t) +g(t). What is the character- istic polynomial of A?
( x Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the...
( x Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: +15y = t 1.C:y(0) = 0.5 Using Euler's method, and a time step of At 0.2. do you expect the numerical solution not to oscillate and to be stable? None of the above. No, because Euler's method is implicit and there is not stability limit on At. Yes, because Euler's method is explicit and there is not stability limit...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3,...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3, u(0)2 = ' dt de g(u, v) -2000u - 1000, v(0)-3 Note that 1 u<2 and -4 <v < 3 for all t. (a) Find the Jacobian matrix for the system of equa tions (b) Find the eigenvalues of the Jacobian matrix. (c) In the figure the shaded region shows the region of absolute stability, in the complex h plane, for third order explicit...
Numerical methods for engineers (30%) ORDINARY DIFFERENTIAL EQUATIONS Solve ODE dy/dx-3xy, where xo-1; yo-2, with step...
Numerical methods for engineers
(30%) ORDINARY DIFFERENTIAL EQUATIONS Solve ODE dy/dx-3xy, where xo-1; yo-2, with step size h-0.1, (calculate only the first point, ie at x,-1.1 yiz?, )using (a) Euler's method (b) Heun's method (b) Fourth-order RK's method 4"
Finite difference methods are also used to approximate the solution to ordinary differential equations. Consider the bo...
Finite difference methods are also used to approximate the solution to ordinary differential equations. Consider the boundary value problem for the general second-order equation with constant coefficients d2y dy dr2 dr Let the interval a x approximations b be divided inton subintervals of width h -(b- a)/n. Using the central difference find the linear system that must be solved to approximate y2.y3.....yn
Finite difference methods are also used to approximate the solution to ordinary differential equations. Consider the boundary value...
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial...
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = 1.C:y(0) = 0.5 Using the results in question 21 and 22, the computed absolute value of the error estimate e for the modified Euler predicted solution using a time step of At = 0.2.is None of the above. Ec-0.12 Ec-0.42 Ec-1.42 Ec-15.42 21 Y(0.2) = 0.5 +0.77=1.27 k, = 0.2 [0.15 (0.5))=-1.5 K2=0.2 [02-151-1)] = 3.04 k=kitky =...
Question 21 1 pts Problem 21: Numerical solution of Ordinary differential equations Consider the following initial...
Question 21 1 pts Problem 21: Numerical solution of Ordinary differential equations Consider the following initial value problem G.EE +15y = 1.C:y(0) - 0.5 Carry out a single step of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.2, and the predicted solutions is Y(0.2)-0.20 None of the above y(0.2)-1.27 Y(0.2)-0.25 (0.2)--0.75
Question is as follows:
NOTE:
• Subject: Numerical Methods for Ordinary Differential
Equations: Initial Value Problems.
______
Useful Information
Implicit Nystrom Method: (aka Milne-Simpson)
Explicit Nystrom Method: (for reference)
Adams-Bashforth Method (AB): (for reference)
Zero-Stability:
Root Condition: (for reference)
3. Consider the 2-step Implicit Nyström Method (aka Simpson's Method): Un+2 – Un = (F(UM) + 4f(Un+1) + f(Un+2)]. (a) Determine the two characteristic polynomials, p() and o(5), for this method. Use these to show that this method is consistent. (b)...
this is numerical analysis. Please do a and b
4. Consider the ordinary differential equation 1'(x) = f(x, y(x)), y(ro) = Yo. (1) (a) Use numerical integration to derive the trapezoidal method for the above with uniform step size h. (You don't have to give the truncation error.) (b) Given below is a multistep method for solving (1) (with uniform step size h): bo +1 = 34 – 2n=1 + h (362. Yn) = f(n=1, 4n-1)) What is the truncation...
Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = + 1.C: y(0) 0.5 Using Euler's method, and a time step of At = 0.2. do you expect the numerical solution not to oscillate and to be stable? No, because the time step far exceeds the critical value At stable < 0.067 for this problem. None of the above Yes, because Euler's method is explicit and there is...
Numerical Methods for Ordinary Differential Equations: Initial
Value Problems
1.10.** Write the IVP x'"' (t) – ax"(t) – bx'(t) – cx = f(t), x(0) = $, s'(0) = n, x"(0) = 5 as a first-order system x'(t) = Ax(t) +g(t). What is the character- istic polynomial of A?
( x Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: +15y = t 1.C:y(0) = 0.5 Using Euler's method, and a time step of At 0.2. do you expect the numerical solution not to oscillate and to be stable? None of the above. No, because Euler's method is implicit and there is not stability limit on At. Yes, because Euler's method is explicit and there is not stability limit...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3, u(0)2 = ' dt de g(u, v) -2000u - 1000, v(0)-3 Note that 1 u<2 and -4 <v < 3 for all t. (a) Find the Jacobian matrix for the system of equa tions (b) Find the eigenvalues of the Jacobian matrix. (c) In the figure the shaded region shows the region of absolute stability, in the complex h plane, for third order explicit...
Numerical methods for engineers
(30%) ORDINARY DIFFERENTIAL EQUATIONS Solve ODE dy/dx-3xy, where xo-1; yo-2, with step size h-0.1, (calculate only the first point, ie at x,-1.1 yiz?, )using (a) Euler's method (b) Heun's method (b) Fourth-order RK's method 4"
Finite difference methods are also used to approximate the solution to ordinary differential equations. Consider the boundary value problem for the general second-order equation with constant coefficients d2y dy dr2 dr Let the interval a x approximations b be divided inton subintervals of width h -(b- a)/n. Using the central difference find the linear system that must be solved to approximate y2.y3.....yn
Finite difference methods are also used to approximate the solution to ordinary differential equations. Consider the boundary value...
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = 1.C:y(0) = 0.5 Using the results in question 21 and 22, the computed absolute value of the error estimate e for the modified Euler predicted solution using a time step of At = 0.2.is None of the above. Ec-0.12 Ec-0.42 Ec-1.42 Ec-15.42 21 Y(0.2) = 0.5 +0.77=1.27 k, = 0.2 [0.15 (0.5))=-1.5 K2=0.2 [02-151-1)] = 3.04 k=kitky =...
Question 21 1 pts Problem 21: Numerical solution of Ordinary differential equations Consider the following initial value problem G.EE +15y = 1.C:y(0) - 0.5 Carry out a single step of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.2, and the predicted solutions is Y(0.2)-0.20 None of the above y(0.2)-1.27 Y(0.2)-0.25 (0.2)--0.75
Most questions answered within 3 hours.
-
a) Draw two water molecules.
b) Clearly name and label the type of bond that exists...
asked 41 minutes ago -
C - Language
Write a loop that sets each array element to the sum of itself...
asked 1 hour ago -
(63
#14)
which of the following statments best describes how chamging
the concentration of the substances...
asked 5 hours ago -
In the following reaction, which element is undergoing
oxidation: Na2SO3 + N2O --> N2 + Na2SO4...
asked 6 hours ago -
Which of the following pairs of ions have the same electron
configuration?
I: Br− and Se2−...
asked 8 hours ago -
The Foremost Composite Materials Company is planning a two-day
sales conference for October 19-20. The conference...
asked 9 hours ago -
3) Illustrate the observed pattern of relatedness of organisms
versus adaptations to specific conditions. This means...
asked 9 hours ago -
In winter a lake has a 0.35 m thick ice layer over 1.10 m of
water....
asked 10 hours ago -
Assuming the following has been encrypted with a Vigenere cipher
below, use the method(s) and assumptions...
asked 10 hours ago -
How would I use switch statements to write a program that will
take an input of...
asked 10 hours ago -
Imagine a reaction in which methane gas combusts at a constant
pressure of 1 atm and...
asked 10 hours ago -
Two parallel wires (each 12 m in length) are separated by a
distance of 0.065 m...
asked 10 hours ago