Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 8.1, Problem 7CP
To determine
To find: The smallest C for which the given population on the patch [0, 10] survives in the long run, Use the Crank-Nicolson method to approximate the solution, and try to confirm that your result do not depend on the step size choice. And to compare the result with the survival rule y13y
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Use t-Test to solve the given problem. Use the
Stepwise method.
Activity 1:
1. To find out whether a new serum would arrest
leukemia, 16 patients, who had all reached an
advanced stage of the disease , were selected.
Eight patients received the treatment and eight
did not. The survival was taken from the time
the experiment was conducted. Use .05 level of
significance. (Problem: Will new serum arrest
leukemia for the 8 patients who had all reached
an advanced stage?)
No Treatment: 2.1, 3.2, 3.0, 2.8, 2.1, 1.2, 1.8, 1.9
With Treatment: 4.2, 5.1, 5.0, 4.6, 3.9, 4.3, 5.2,
3.9
Based on long-term investigation, researchers have suggested that the acidity (pH) of rainfall in the Shenandoah Mountains can be described by the Normal model N(4.9, 0.6). Show your work while answering the following questions
Two manufacturing companies of soap each claims that their product is superior in whitening one’s complexion. A researcher did an experiment by randomly choosing two groups and assigning each group to use the product for one month. Results are shown below where the higher the number, the more effective the product in skin whitening. At (t-tabular value is ) level, is there a significant difference between the two products effectiveness in skin whitening?
Product (Soap A or B)
A
10 12 13 13 15 15 15 17 18 24 25 25 25 27 28 30 30
B
8 9 11 15 16 16 16 19 20 21 25 25 26 28 29 30 30 32 33 33
Chapter 8 Solutions
Numerical Analysis
Ch. 8.1 - Prove that the functions (a) u(x,t)=e2t+x+e2tx,...Ch. 8.1 - Prove that the functions (a) u(x,t)=etsinx, (b)...Ch. 8.1 - Prove that if f(x) is a degree 3 polynomial, then...Ch. 8.1 - Prob. 4ECh. 8.1 - Verify the eigenvector equation (8.13).Ch. 8.1 - Show that the nonzero vectors vj in (8.12 ), for...Ch. 8.1 - Prob. 1CPCh. 8.1 - Consider the equation ut=uxx for 0x1, 0t1 with the...Ch. 8.1 - Prob. 3CPCh. 8.1 - Use the Backward Difference Method to solve the...
Ch. 8.1 - Use the Crank-Nicolson Method to solve the...Ch. 8.1 - Prob. 6CPCh. 8.1 - Prob. 7CPCh. 8.1 - Setting C=D=1 in the population model (8.26), use...Ch. 8.2 - Prove that the functions (a) u(x,t)=sinxcos4t, (b)...Ch. 8.2 - Prove that the functions (a) u(x,t)=sinxsin2t, (b)...Ch. 8.2 - Prove that u1(x,t)=sinxcosct and u2(x,t)=ex+ct are...Ch. 8.2 - Prove that if s(X) is twice differentiable, then...Ch. 8.2 - Prove that the eigenvalues of A in (8.33) lie...Ch. 8.2 - Let be a complex number. (a) Prove that if +1/ is...Ch. 8.2 - Solve the initial-boundary value problems in...Ch. 8.2 - Solve the initial-boundary value problems in...Ch. 8.2 - Prob. 3CPCh. 8.2 - Prob. 4CPCh. 8.3 - Show that u(x,y)=ln(x2+y2) is a solution to the...Ch. 8.3 - Prob. 2ECh. 8.3 - Prove that the functions (a) u(x,y)=eysinx, (b)...Ch. 8.3 - Prove that the functions (a) u(x,y)=exy, (b)...Ch. 8.3 - Prove that the functions (a) u(x,y)=sin2xy, (b)...Ch. 8.3 - Prove that the functions (a) u(x,y)=ex+2y, (b)...Ch. 8.3 - Prob. 7ECh. 8.3 - Show that the barycenter of a triangle with...Ch. 8.3 - Prove Lemma 8.9 .Ch. 8.3 - Prove Lemma 8.10.Ch. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Solve the Laplace equation problems in Exercise 3...Ch. 8.3 - Prob. 2CPCh. 8.3 - Prob. 3CPCh. 8.3 - Prob. 4CPCh. 8.3 - Prob. 5CPCh. 8.3 - The steady-state temperature u on a heated copper...Ch. 8.3 - Prob. 7CPCh. 8.3 - Prob. 8CPCh. 8.3 - Solve the Laplace equation problems in Exercise 3...Ch. 8.3 - Solve the Poisson equation problems in Exercise 4...Ch. 8.3 - Solve the elliptic partial differential equations...Ch. 8.3 - Prob. 12CPCh. 8.3 - Prob. 13CPCh. 8.3 - Solve the elliptic partial differential equations...Ch. 8.3 - Prob. 15CPCh. 8.3 - Prob. 16CPCh. 8.3 - For the elliptic equations in Exercise 7, make a...Ch. 8.3 - Solve the Laplace equation with Dirichlet boundary...Ch. 8.4 - Show that for any constant c, the function...Ch. 8.4 - Show that over an interval [ x1,xr ] not...Ch. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 1CPCh. 8.4 - Prob. 2CPCh. 8.4 - Solve Fishers equation (8.69) with...Ch. 8.4 - Prob. 4CPCh. 8.4 - Solve the Brusselator equations for...Ch. 8.4 - Prob. 6CP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?arrow_forwardQ6.6. Imagine that a new, deadly coronavirus arises and starts a global pandemic. Experts are worried because the disease spreads easily, having a basic repréductive number, R 0, of 5. The good news is that an effective vaccine is quickly developed. What proportion of the population, P, would need to be vaccinated to ensure that the disease can no longer spread?arrow_forwardNationally, 60.2% of federal prisoners were serving time for drug offenses in 2015. A warden feltthat in his prison the percentage was even higher. He surveyed 400 inmates’ records and foundthat 260 of the inmates are drug offenders. At α = 0.10, is he correct?arrow_forward
- lecture(12.11): Researchers were interested in the effects of co-sleeping on nightime waking and crying in infants. .They assesed the number of minutes parents reported that their infants were awake and crying for a period of three days. Five of the infants co-slept with thier mothers(Co) and four infants slept in crib(Cr).The researchers wanted to see if there was a difference in the total number of minutes of crying during the 3 nights. for the two groups. A summary of the data is given below Co-sleepers night time crying in minutes: 8, 4, 7, 7, 6 Crib-sleepers night time crying in minutes: 30, 17, 22, 25 Test the hypotheses at (aplha=.05) level of signifcance. using the 5 step hypotheses testing procedure. Clealy state the null and alternative hypotheses. Round your answer to 2 decimal places.arrow_forwardP(t) = 24 + 0.4t. What are the values of the population for t = 10, 20, and 30?arrow_forwardYou have noticed that UMD students seem to drink more coffee (on average) the longer they have been in school. To study this question, you survey 200 students and obtain their average weekly coffee intake. Data are collected using a between-subjects approach on 50 Freshmen, 50 Sophomores, 50 Juniors, and 50 Seniors. The data are presented in terms of how many cups of coffee, on average, each class drank per week. Here is what was found: Freshmen (M= 11.5, SD=3.1) Sophomore (M= 12.1, SD=2.2) Junior (M= 15.3, SD=2.5) Senior (M-19.8, SD=3.0) F(3,196)= 6.5, p = .004, n² = .32, Tukey's HSD = 2.4 Based on the nature of the independent variable and design of the study, what statistical test should have been used? OA. Dependent (paired samples) t-test OB. One-way ANOVA OC. Independent samples t-test Save Answer O D. Repeated Measures ANOVAarrow_forward
- A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 231 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 230,233, 235, 236, 233, 240, 240, 241, and 237. Using α = 0.025, has the shelf life of the cake mix increased? Multiple Choice Yes, because computed t is greater than the critical value. Yes, because computed t is less than the critical value. No, because computed t lies in the region of acceptance. No, because 236.11 is quite close to 231.arrow_forwardIf u = x1x2 + x2x3+ X3X1, then find the relative percentage error in the computation of u at x1 = 2.104, x2 1.935 and x3= = 0.845.arrow_forwardA research study comparing three treatment conditions produces T=20 with n=4 for the first treatment, T=10 with n=5 for the second treatment, and T=30 with n=5 for the third treatment. Calculate SSbetween treatments for this data.arrow_forward
- A sample of 3 hospitals was selected, and the number of infections for a specific year has been reported.At x = 0.05 can it be concluded that the number of infections is related to the hospital where they occurred? Please use R software.arrow_forwardQ1 The owner of the ABC garment is interested to study the wastage of the factory. Factory is running in two shifts (morning and evening). The value of the monthly wastage of the material shift wise is given in the data file. The manager told to the owner that on average, the value of monthly (both shifts) wastage is Rs. 4500. The owner feels that the wastage is more than the value which is communicated by the manager; therefore, he gives the data of the last few months (given below) to you as statistician and assigns the following three tasks: Morning Shift 4227 4489 4417 4392 3943 3970 4405 4990 4444 4405 4398 4152 Evening Shift 3366 2964 3043 3804 3721 3675 3504 3236 3955 3420 Task # 1: To test the manager’s claim at 0.05 level of significance. Task # 2: To test the equality of mean wastage in two shifts, assume the variances are equal at 0.05 level of significance.…arrow_forwardEvaluate C and P4. pune 4. 11 C3D 11 3 7 4 %3D | = *a+arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License