数值分析作业代写 Numerical Analysis Problem 1

Numerical Analysis

数值分析作业代写  Execute the command“format long”to obtain output with more digits. Use cut and-paste to copy results with different step

Problem 1.  数值分析作业代写

(1)(5 points) Compute the solution up to timet=1.0 ofthe problem
dy
dt=4y(1-y),0≤t≤1, y(0)=0.05

using both Euler’s method and the Runge-Kutta method qiven in Problem1/i.eModified Euler's method).Use step size h=02010.050025001250.006250.003125and record the value of the solutionatt=1.0.

Tip: Execute the command“format long”to obtain output with more digits. Use cut and-paste to copy results with different step sizes,oralternately do the computations within a loop over different step sizes, capture the solution at the final times in an array and then print out the values.  数值分析作业代写

(2)(5 points)Verify the order ofaccuracy ofboth of your methods(Euler's method and Runqe-Kutta method qiven in Problem 1)i.e.Modifed Euler’s method by using Atkin- son estimation on each set of three consecutive solution values you computed in above question. Turn in your estimates(Check the notes ofestimating p on April 12). [Tip:If you ’ve captured the final time values with different step sizes in an array, one can write a loop to estimate and print out the estimated rates of converqence for each set of three consecutive values.

(3)(5 points) Find the analytic solution of the problem in(1).Compute and record the value of the analytic solution at timet=1.0.(Write down the process as detailed as possible)  数值分析作业代写

(4) (5 points)Use the value of the analytic solution at timet=10 which is computed in part 3 to calculate the absolute errors ofboth methods(Euler’s method and Runge Kutta method qiven in Problem 1)(i.e.Modifed Euler's method) at t=1.0 with h02010050.0250.01250006250.003125. Use a table to show the absolute errors of both methods. Remark 4. Please print out your code and results for Problem 3) part 124.

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