Could you explain in depth what the question is asking and have clear steps so I can understand the code, which should be in c++Thank you! This exercise will make use of numerical integration to get a solution to an ordinary differ-ential equation (ODE). We will solve the ODE,dydt=(1)This particular equation could be a model for reactions in chemistry, biology and evenastrophysics. 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 remainingreactants (1-y) nH₂/n2,ini2,initial and other factors included in a. In practice a would be afunction of the environment (temperature, density, etc...) but for simplicity we will keep aconstant. We will start from y(0) = 0. This ODE then has the following exact, analyticalsolution 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 analyticalsolutions. The choice of solver requires considering complexity, stability and accuracy (smallerrors!). 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 notesabout PGPLOT for more information.You can use ploty.cpp and its Makefile from /home/2G03/ploty as a basis to do thisexercise. 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 calleddydt to evaluate it for specific input y and a values. Call it when you need the rate of changeof y throughout this homework. You can keep the function and the main program in one filein 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 mainprogram that calls the function dydt. The main program should call it with the argumentsy = 0.5 and a = 0.04 and y = 0.2 and a = 0.4. Use cout to print the values to the terminal.1Compile and link testdydt.cpp into a program called testdydt. The program only needs to dothe test and nothing else. Report the rates from your program for these cases, dydt (0.5, 0.04)and dydt (0.3,0.3).

Answered: Compile and link testdydt.cpp into a…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Question

Could you explain in depth what the question is asking and have clear steps so I can understand the code, which should be in c++

Thank you!

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).

Expert Solution

Step 1: Providing Introduction

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.

Step by step

Solved in 6 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions