Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 6.7, Problem 12E
The Mime-Simpson Method is a weakly stable fourth-order, two-step implicit method. Are there any weakly stable third-order, two-step implicit methods?
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Original: 100-200 = 20,000
200400=20,000 80
602=3600 694761
=4
4x1.3225-6.29
4761/3600 = 1-3225 5.29-1058msy
6). The dose to the body was 200 mSv. Find
the dose to the lung in mrem?
W 200ms
20
2.15
and
8) A technique of 20 mAs, 40 kV produces a
f4 Sy Find the dose to the Thyroid in
Chapter 6 Solutions
Numerical Analysis
Ch. 6.1 - Show that the function y(t)=tsint is a solution of...Ch. 6.1 - Show that the function y(t)=esint is a solution of...Ch. 6.1 - Use separation of variables to find solutions of...Ch. 6.1 - Find the solutions of the IVP given by y(0)=0 and...Ch. 6.1 - Apply Eulers Method with step size h=1/4 to the...Ch. 6.1 - Apply Eulers Method with step size h=1/4 to the...Ch. 6.1 - (a) Show that y=tan(t+c) is a solution of the...Ch. 6.1 - (a) Show that y=tanh(t+c) is a solution of the...Ch. 6.1 - For which of these initial value problems on [0,...Ch. 6.1 - Sketch the slope field of the differential...
Ch. 6.1 - Find the solutions of the initial value problems...Ch. 6.1 - (a)Show that if a0, the solution of the initial...Ch. 6.1 - Use separation of variables to solve the initial...Ch. 6.1 - Find the solution of the initial value problem...Ch. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Apply Eulers Method with step size h=0.1 on [0, 1]...Ch. 6.1 - Plot the Eulers Method approximate solutions for...Ch. 6.1 - Plot the Eulers Method approximate solutions for...Ch. 6.1 - Prob. 4CPCh. 6.1 - For the IVPs in Exercise 4, make a log-log plot of...Ch. 6.1 - Prob. 6CPCh. 6.1 - Plot the Eulers Method approximate solution on [0,...Ch. 6.1 - Plot the Eulers Method approximate solution on [0,...Ch. 6.1 - Calculate the Eulers Method approximate solution...Ch. 6.1 - Calculate the Eulers Method approximate solution...Ch. 6.1 - Plot the Eulers Method approximate solution on [0,...Ch. 6.2 - Using initial condition y(0)=1 and step size...Ch. 6.2 - Using initial condition y(0)=0 and step size...Ch. 6.2 - Find the formula for the second-order Taylor...Ch. 6.2 - Apply the second-order Taylor Method to the...Ch. 6.2 - (a) Prove (6.22) (b) Prove (6.23).Ch. 6.2 - Apply the Explicit Trapezoid Method on a grid of...Ch. 6.2 - Prob. 2CPCh. 6.2 - Prob. 3CPCh. 6.2 - Prob. 4CPCh. 6.2 - Prob. 5CPCh. 6.2 - Plot the Trapezoid Method approximate solution on...Ch. 6.2 - Calculate the Trapezoid Method approximate...Ch. 6.2 - Calculate the Trapezoid Method approximate...Ch. 6.2 - Prob. 9CPCh. 6.3 - Apply the Eulers Method with step size h=1/4 to...Ch. 6.3 - Apply the Trapezoid Method with h=1/4 to the...Ch. 6.3 - Convert the higher-order ordinary differential...Ch. 6.3 - Apply the Trapezoid Method with h=1/4 to the...Ch. 6.3 - (a) Show that y(t)=(et+ett2)/21 is the solution of...Ch. 6.3 - Apply Eulers Method with step sizes h=0.1 and 0.01...Ch. 6.3 - Carry out Computer Problem 1for the Trapezoid...Ch. 6.3 - Prob. 3CPCh. 6.3 - Prob. 4CPCh. 6.3 - Prob. 5CPCh. 6.3 - Adapt pend.m to build a damped pendulum with...Ch. 6.3 - Prob. 7CPCh. 6.3 - Prob. 8CPCh. 6.3 - Prob. 9CPCh. 6.3 - Prob. 10CPCh. 6.3 - Prob. 11CPCh. 6.3 - Prob. 12CPCh. 6.3 - Prob. 13CPCh. 6.3 - Prob. 14CPCh. 6.3 - Prob. 15CPCh. 6.3 - A remarkable three-body figure-eight orbit was...Ch. 6.4 - Apply the Midpoint Method for the IVPs...Ch. 6.4 - Carry out the steps of Exercise 1 for the IVPs...Ch. 6.4 - Apply fourth-order Runge-Kutta Method to the IVPs...Ch. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Consider the initial value problem y=y . The...Ch. 6.4 - Prob. 7ECh. 6.4 - Prob. 1CPCh. 6.4 - Apply the fourth-order Runge-Kutta Method solution...Ch. 6.4 - Carry out the steps of Computer Problem 2, but...Ch. 6.4 - Prob. 4CPCh. 6.4 - Plot the fourth-order Runge-Kutta Method...Ch. 6.4 - Plot the fourth-order Runge-Kutta Method...Ch. 6.4 - Prob. 7CPCh. 6.4 - Prob. 8CPCh. 6.4 - Prob. 9CPCh. 6.4 - Prob. 10CPCh. 6.4 - Adapt the orbit .m MATLABs program to animate a...Ch. 6.4 - Assess the conditioning of the Lorenz equations by...Ch. 6.4 - Follow two trajectories of the Lorenz equations...Ch. 6.4 - Prob. 14CPCh. 6.4 - Prob. 15CPCh. 6.4 - Prob. 16CPCh. 6.4 - Prob. 17CPCh. 6.4 - Prob. 18CPCh. 6.4 - Run tacoma.m with wind speed W=80km/hr and initial...Ch. 6.4 - Replace the Trapezoid Method by fourth-order...Ch. 6.4 - The system is torsionally stable for W=50km/hr ....Ch. 6.4 - Find the minimum wind speed W for which a small...Ch. 6.4 - Prob. 5SACh. 6.4 - Prob. 6SACh. 6.4 - Prob. 7SACh. 6.5 - Write a MATLAB implementation of RK23 (Example...Ch. 6.5 - Prob. 2CPCh. 6.5 - Prob. 3CPCh. 6.5 - Compare the results of Computer Problem 3 with the...Ch. 6.5 - Apply a MATLAB implementation of RKF45 to...Ch. 6.6 - Using initial condition y(0)=0 and step size...Ch. 6.6 - Find all equilibrium solutions and the value of...Ch. 6.6 - Prob. 3ECh. 6.6 - Consider the linear differential equation y=ay+b...Ch. 6.6 - Apply Backward Euler, using Newtons Method as a...Ch. 6.6 - Carry out the steps in Computer Problem1 for the...Ch. 6.7 - Apply the Adams-Bashforth Two-Step Method to the...Ch. 6.7 - Carry out the steps of Exercise 1 on the IVPs...Ch. 6.7 - Prob. 3ECh. 6.7 - Prob. 4ECh. 6.7 - Show that the Implicit Trapezoid Method (6.89) is...Ch. 6.7 - Prob. 6ECh. 6.7 - Prob. 7ECh. 6.7 - Prob. 8ECh. 6.7 - Find the order and stability type for the...Ch. 6.7 - Prob. 10ECh. 6.7 - Prob. 11ECh. 6.7 - The Mime-Simpson Method is a weakly stable...Ch. 6.7 - Prob. 13ECh. 6.7 - (a) Use the matrix formulation to find the...Ch. 6.7 - Prob. 15ECh. 6.7 - (a) Use the matrix formulation to find the...Ch. 6.7 - Adapt the exmultistep.m program to apply the...Ch. 6.7 - Adapt the exmultistep.m program to apply the...Ch. 6.7 - Prob. 3CPCh. 6.7 - Prob. 4CPCh. 6.7 - Prob. 5CPCh. 6.7 - Prob. 6CPCh. 6.7 - Prob. 7CPCh. 6.7 - Prob. 8CPCh. 6.7 - Prob. 9CPCh. 6.7 - Change Program 6.8 into a fourth-order...
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- original ssD 400x (100) 2 400 x (14)=100 34 10or (2)² = 100 × (0-85) = 100 x = 72.25 100x 40 72.25 =36.13 500 36.13 13.84 O. 7225 12x13.84≈ 166.08mAs 10) The dose of a radiograph was 100 mSv with a technique of: 10 mAs, 180 kV at 200 cm and tabletop. If the technique is changed to: 20 mAs, 153 kV at 100 cm using a 5:1 grid then find the new dose in rem to the Lungs. 11) A radiographic technique produces an exposure index of EI= 300 and TEI=600 at a source- to-image receptor distance (SID) of 200 cm, 100 kV, 5:1 grid using 10 mAs. If the technique is changed to 100 cm and 85 kV and 5 mAs with table top find the new exposure index? What is the value of DI? 10arrow_forwardexam review please help!arrow_forward0. 75 and 34 KV arved fromise to 75 halfed NAME Genesis Ward 0 mAs is 40 #2). A technique involves 150 mAs, 40 kV and produces an intensity of 2 R. are gone down KV C15%! In = 200% Find the new intensity in mGya, using 300 mAs and 46 kV? =100 206a 150mAS 40KV 2R kv 150 is so divide 00 mA, 200 alue of 100. Boomts 46KY 4). A technique is taken with 100 mA, 200 ms, 60 kV and produces 200 mSv.arrow_forward
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