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The following tridiagonal system must be solved as part of a larger algorithm (Crank-Nicolson) for solving partial differential equations:
Use the Thomas algorithm to obtain a solution.
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Chapter 11 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- If possible solve it in a paperarrow_forwardSolve. 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 system of differential equations x₁ = 10/3x₁ +4/3x2 x2 = 8/3x1 +14/3x2 9 where 1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution.arrow_forward
- Consider 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_forwardWrite the system of differential equations given in the 1st photo in the normal form defined in the 2nd photo and solve the resulting system by means of the eigenvalues and eigen-vectors of the square matrix A.arrow_forwardFor each of the following systems of differential equations, use the eigenvalues and eigenvectors of the coefficient matrix to find the general solution. A. B. *1-2x17x2 2x14x2 = *1 = 2x1 *2 = 5x2 - 7x3 *3 = 2x₂ - 4x3arrow_forward
- Consider the system [BAH[3] = 21 (a) Use the starting guess X(0) 1.5 show that X(¹) -([4] = Find X (2) and X (3) (b) Use the starting guess X(0) to show that X(¹) = = 1.5 -3.25 A in an implementation of the Jacobi method to in an implementation of the Gauss-Seidel method Find X(²) and X (3)arrow_forwardSolve the system x2 + y – 4.5 = 0 -In x + y – 1.5 = 0 using the Newton-Raphson method, starting from the point (Xo = 1.1, yo = 1.1), and detailing all the steps of the iterative calculation. (Convergence to 8 decimal places). %3Darrow_forwardApply the eigenvalue method of this section to find a general solution of the given system. If initial values are given, use graphing calculator to construct a typical solution curves for the given system. x = 9x1 + 5x2 х 3 — 6х1 — 2х2 X1 (0) = 1, x2(0) = 0arrow_forward
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