2. Write a program to apply the Euler's method to solve the initial value problem y' – 2y = 4t; y(0) = 2 Find the numerical solution at t = 1 and compare with the exact solution. Verify the order of accuracy by using different step sizes: h=+1 1 1 10 20' 40 ' 80*
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- You are working on a problem where the size of each test case is between 1 and 100 integers and where the timeout is 4 seconds.You have developed a cubic time algorithm for the problem that gives the correct answeron all test cases.If you submit that solution, will you pass all test cases in time?Please answer YES or NO and then briefly explain your answer.In Python, grades_dict = {'Wally': [87,96,70], 'Eva': [100,87,90], 'Sam': [94,77,90], 'Katie': [100,81,82], 'Bob': [83,65,85]} Write your own describe function that produces the same 8 statistical results, for each one of the columns, that the built-in describe() function does. Note 1: Use the sample standard deviation formula (that is, the denominator is: N-1) Note 2: Your algorithm should work for any number of columns not just for 5 Note 3: You can use the np.percentile() for the 25% and 75% percentile as well as the sort() built-in functionsPYTHON: Write a program (without using built-in functions from scipy, etc) to find the roots of the equation: x - 1.5 - 0.5sin(x) = 0 by the Newton-Raphson method. Solve for roots within the interval 0 < x < 2pi. Plot the error as a function of iteration number to see how quickly it converges.
- Euler's method is a numerical method for generating a table of values (xi, yi) that approximatethe solution of the differential equation y' = f(x,y) with boundary condition y(xo) = yo. The firstentry in the table is the starting point (xo , yo.). Given the entry (xi , yi ), then entry (xi+1 , yi+1) isobtained using the formula xi+1 = xi + x and yi+1 = yi + xf(xi , yi ). Where h is the small valuecalled step size. use c++ code and Use Euler's method to estimate the value of y when x = 2.5 for the solution of the differentialequation y' = x + 3y/x with the boundary condition y(1) = 1. Take x = 0.1, the exact solution ofthis differential equation is y = 2x^3- x^2.. Compare your approximation values with the exact value.Typically, the clearest way to explain an algorithm is in English, with the use of some notation. A clear explanation followed by annotated pseudo-code is also fine. pls send me solution fast within 5 minutes and i will like for sure. solution musst be in typed form. Remember that when a problem asks you to design an algorithm, you must also prove the algorithm’s correctness and analyze its running time, i.e., the running time must be bounded by a polynomial function of the input size.Write a C++ program to solve ?(?) = 2? − (? + 4)^ 0.5. Apply Newton’s Method where the initial value is 1 and continue the process until two successive approximations differ by less than 0.001. Output: Enter the Initial Value: 1 Iteration Number: 1
- What is the effect in the time required to solve a problem when you increase the size of the input from n ton + 1, assuming that the number of milliseconds the algorithm uses to solve the problem with input size n iseach of these functions? [Express your answer in the simplest form possible, either as a ratio or a difference. Youranswer may be a function of n or a constant.]a) log n b) 100n c) n^2 d) 2^n e) n!Let us design a Monte Carlo method to estimate the area of the shadow region under the green function y = ex when x is from 0 to r. As shown in the following figure, r is a variable (r> 0) for range. Please write a Python program named "A1Q1_MonteCarlo.py" to implement your designed Monte Carlo method. In the first line of your code, please write "n=10000" to define n as the experiment number of random sampling. Finally, please print out the estimated area for different range variables with the following format: When r=1, estimated shadow area is xxx When r=2, estimated shadow area is xxx When r=9, estimated shadow area is xxx When r=10, estimated shadow area is xxx [Hint]: You may need to use a loop for different range variables r and generate random sampling points automatically based on different range variables r.write a computer program that uses newtons method to find the root of a given function. and apply this program to find the root of the followig functions, using X0 as given . stop the iteration when the error as estimated by |Xn+1- Xn| is less than 10-6 . compare to your result for bisection.(a) f(x)=1-2xe-×/2 , X0=0; (b) f(X)=5-x-1, x0=1/4; (c) f(x)=x3-2x-5, x0=2; (d) f(x)=ex-2, x0=1; (e) f(x)=x-ex, x0=1; (f) f(x)=x6 - x -1, x0=1; (g) f(x)=x2 -sin x, x0=1/2; (h) f(x)=x3 - 2, x0=1; (i) f(x)=x+ tan x, x0=3; (j) f(x)=2 - x-1lnx , x0=1/3;
- Create an excel program that can solve an engineering non-linear equation using thefollowing methods. You can choose your own non-linear equation. Make sure to explain whatis the use of the equation. a) Bisection Method (200 iterations) (15%)b) Regula Falsi / False-Position Method (200 iterations) (15%)c) Simple Fixed Point Iteration (200 iterations) (15%)d) Newton Raphson method (200 iterations) (15%The finite difference method transforms the ordinary differential equation in a system of linear equations of the form with k=1,2,...,(n−1) , h=1/n, y0=0 and yn=5 . Knowing this, make n=5 and assemble the associated linear system. Then solve numerically using some iterative method and compare the numerical solution with the exact analytical solution y(x)=x^4+4x . So do the same for n=10 and comment on what you observed. code with python.In Python, grades_dict = {'Wally': [87,96,70], 'Eva': [100,87,90], 'Sam': [94,77,90], 'Katie': [100,81,82], 'Bob': [83, 65, 85]} write your own describe function that produces thesame 8 statistical results, for each one of the columns, that the built-in describe() function does.Note 1: Use the sample standard deviation formula (that is, the denominator is: N-1)Note 2: Your algorithm should work for any number of columns not just for 5Note 3: You can use the np.percentile() for the 25% and 75% percentile as well as the sort()built-in functions