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The following tridiagonal system must be solved as part of a larger algorithm (Crank-Nicolson) for solving partial
Use the Thomas algorithm to obtain a solution.
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Chapter 11 Solutions
Numerical Methods for Engineers
- Solve Exercise 14 if a 25 solution of the same mixture is added instead of pure alcohol.arrow_forwardIn 6 decimal places and in 8th iteration, use the Gauss-Seidel iterative process to find the solution of x, in the following system of equations 1.2.x1 + 4.4.x2 – 1.9x3 = -4.2 5.1x1 – 1.3x2 +2.4x3 = 2.7 -2.6.x1 + 1.7x2 – 6.3.x3 = 9.6. (0) (0) (0) Use x, = X2 = x3 = 1 (8) Answer: X3arrow_forwardtion 1.7 For this system of two equations y = cos² (x), x² + y² = x = 2, = a. Plot the two equations and observe two intersections that occur near x 2 and x -1. b. Substitute y from the first equation into the second getting an equation in only x. Solve this equation for the x-value (s) by any of the methods in this chapte to find where the function is zero, then substitute this x-value in either of the original equations to ge y-values. - . Repeat part (b) but now solve for x from one equa tion and use it to eliminate x from the other. You should get the same solutions, of course, but which is easier to use?arrow_forward
- Find all solutions of x2 - x + 2 = 0 over Z3[i].arrow_forwardInitially, two large tanks A and B each hold 100 gallons of brine. The well-stirred liquid is pumped between the tanks as shown in the figure below. Use the information given in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time t, measured in minutes, in tanks A and B, respectively.arrow_forwardFind the general solution of the given DEs.arrow_forward
- Suppose Ct is the concentration of a drug in the bloodstream at time t, A is the concentration of the drug that is administered at each time step, and k is the fraction of the drug metabolized in a time step. (a) What is the recursion that models the dynamics of drug concentration? Ct+1 = (b) If the initial concentration is Co 200 150 100 50 200 150 100 50 Ct Ct 2 2 4 = 110 µg/mL and A = 80 µg/mL and k = 6 8 …... 6 CO 8 10 t 10 120 100 80 60 40 20 150 Ct 100 1 2' 50 plot some points on the graph of Ct. 2 2 4 4 8 6 ….... 10 8 t 10arrow_forward2. (a) Show that 25 – 32 = (z – 2)(16 + 8z + 4z² + 2z³ + z4). %3D (b) Find the roots of 16+ 8z + 4z2 + 223 + z4 = 0 by using De Moivre's theorem to solve 25 – 32 = 0. -arrow_forwardLK [] Rk the number of owls in the area studied, and R is the number (in thousands) of wood rats in the area studied. Suppose Lk + 1 = (0.3)Lk + (0.6)Rk and Rk+ 1 = (-0.2)Lk +(1.1)Rk. Determine the evolution of this system. (Give a formula for XK.) Does the owl population grow or decline? Does the wood rat population grow or decline? Denote owl and wood rat populations in a particular area at time k by xk = Give a formula for xk for this system. Choose the correct answer below. (0.5) 1 [3]+၈] [13]. [:] kqtx[]•gaz[3] + C₂ (0.3) k C₁(1.1) k []+200 [³] (0.5) O A. Xk=C(0.9)k| <-mer O B. Xk=c,(1.1)k| O C. O D. X = C,(0.9)k| where k is the time in months, Lk isarrow_forward
- Solve. The same way to ask the solution Compute the matrix exponential e At for the system x' = Ax given below. - x'₁ =20x₁ −20x₂, x'2 = 10x₁ − 10x₂ e At = 44This is a solved question At Compute the matrix exponential e for the system x' = Ax given below. x₁20x₁20x₂, x 2 = 15x₁15x₂ −3+4e5t 4-4 e 5t At -3+3e5t 4-3 e 5t 1arrow_forwardConsider the following system of coupled second-order equations, x + 4x1 = x2 x2 + 4x2 0. Re-write this system of second order equations as a system of first order equations. Compute the solution for the initial condition x1(0) = 1, x1(0) = 0, x2(0) compute the (complex) Jordan normal form for the system. Note: you should find that the solution grows linearly in time which is indicative of a resonance in the system. = 1, x2(0) 0. Thenarrow_forwardcompute the general solution of the given equationarrow_forward
Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage