Answered: Compile and link testdydt.cpp into a program called testdydt. The program only needs to do the test and nothing else. Report the rates from your program for...

Transcribed Image Text:This exercise will make use of numerical integration to get a solution to an ordinary differ- ential equation (ODE). We will solve the ODE, dy dt = (1) This particular equation could be a model for reactions in chemistry, biology and even astrophysics. y would represent something that is being created from a finite supply of reactants. For example, it might measure the end product of a chemical reaction like 2 H2 + O2 → 2 H2O. Here we would have y = nH2O/nH2,initial. The reaction rate is proportional to the remaining reactants (1-y) nH2/n2,ini 2,initial and other factors included in a. In practice a would be a function of the environment (temperature, density, etc...) but for simplicity we will keep a constant. We will start from y(0) = 0. This ODE then has the following exact, analytical solution which is convenient for checking our answers, y(t)=1-e = a(1 — y). -a t (2) In general, numerical solvers can handle highly non-linear ODEs that do not have analytical solutions. The choice of solver requires considering complexity, stability and accuracy (small errors!). In general more accuracy requires smaller steps or a better method. In this homework we will make use of the PGPLOT library. Please refer to the lecture notes about PGPLOT for more information. You can use ploty.cpp and its Makefile from /home/2G03/ploty as a basis to do this exercise. Remember to change the names in the Makefile. 1.1 We will use the exact expression (equation 1) for din our code. Write a function called dydt to evaluate it for specific input y and a values. Call it when you need the rate of change of y throughout this homework. You can keep the function and the main program in one file in all the exercises. The function declaration should look like: double dydt ( double y, double a) Note that the rate does not depend on explicitly on t so you do not need t as an argument, just y and a. In a file called testdydt.cpp, include your function code and also write a simple main program that calls the function dydt. The main program should call it with the arguments y = 0.5 and a = 0.04 and y = 0.2 and a = 0.4. Use cout to print the values to the terminal. 1 Compile and link testdydt.cpp into a program called testdydt. The program only needs to do the test and nothing else. Report the rates from your program for these cases, dydt (0.5, 0.04) and dydt (0.3,0.3).

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In order to implement the given task in cpp, follow the steps mentioned in the algorithm provided in the next section correctly.

Here, we are tasked with solving an ordinary differential equation (ODE) that represents a rate of change, often seen in various fields, including chemistry and biology.

The ODE, dy/dt = a(1 - y), is a model for reactions where 'y' represents the final product derived from reactants. We'll create a C++ program to calculate dy/dt using the dydt function. The program will then test this function with specific values of 'y' and 'a'. By implementing this, it is possible to gain insights into how to numerically solve ODEs and ensure accuracy in our calculations.

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Compile and link testdydt.cpp into a program called testdydt. The program only needs to do the test and nothing else. Report the rates from your program for these cases, dydt (0.5,0.04) and dvdt (0.3.0.3).

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