(1) Answer True or False to the following questions: [ 4 points] a)1 pt Any solution...
please show excel formulas for both explicit and implicut
methods
please solve using excel and show formulas You are given the following system of differential equations: 99x, +2999x 2000x1 - 3000x2 If x1(0)=x2(0)-1, obtain a solution from t=0 to 0.3 using a step size of 0.03 with a. The explicit Euler's method b. The implicit Euler's method (note that this problem can be solved via a set of simultaneous linear equations for each time step) C. Plot all results on...
( 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...
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...
Given the following non-linear boundary value problem
Use the shooting method to approximate solution
Use finite difference to approximate solution
Plot the approximate solutions together with the exact solution
y(t) = 1/3t2 and discuss your results
with both methods
Question 14 (12 marks) Consider the following separable differential equation. dy cos(z)(-1) dr (a) Find any constant solutions of this differential equation and hence write down the solution with initial value y=- when r=7 (b) Use partial fractions to evaluate 1 dy. 1 (c) Use the method for solving separable differential equations to solve this DE in the case where y 0 when r T. You may assume that the solution does not cross the constant solutions you found in...
2. True (T) or False (F) a) Round-off errors increase with the number of calculations performed b) Newton-Raphson method always converge c) Romberg formula is one of the most popular method for numerical integration d) The error of fourth order Runge-Kutta method is greater than the error of Heun method e) First order Runge-Kutta method is equivalent to the Euler method 1) A system of 2 ordinary differential equations requires 2 initial conditions to be solved g) Gauss quadrature formula...
1. (4 points) Determine whether the given function y, given explicit or implicit, is a solution to the corresponding differential equation a) y = 2* +3e2a; y" - 3y + 2y = 0. dy 2.ry b) y - In y = r2+1, (Use implicit differentiation) dr y-1 2. (3 points) Find the solution to the initial value problem: dy = e(t+1); y(2) = 0 dr 3. (3 points) Find the general solution to the following equation. y dy ada COS
(1 pt) True False Problem Enter T or F depending on whether the statement is true or false. (You must enter T or F True and False will not work.) exists, then the product A-B gives 1. If AX = B represents a system of linear equations and the solution to the system 2. If A and B are both square matrices such that AB equals BA equals the identity matrix, then B is the inverse matrix of A.
1. (10 points, part I) Consider the following initial boundary value problem lU (la) (1b) (1c) 0L, t> 0 3 cos ( a(x, 0) (a) Classify the partial differential equation (1a) (b) What do the equations (la)-(1c) model? (Hint: Give an interpretation for the PDE, boundary conditions and intial condition.) c) Use the method of separation of variables to separate the above problem into two sub- problems (one that depends on space and the other only on time) (d) What...
Please answer the following questions that a person new to this
course would be able to understand.( Include theorem.)
Problem 6: Consider the linear systems of differential equations a) Sketch the direction Seld for the line gystem. write StreamPlotl(x-2y, 2x-3y] İn Wolframı Alpha a) Use the method of elimination to find a second order linear differential equation that is satisfied by (t b) Find particular solutions x(t) and y(t) such that x(0) 1 and y(0) 2