Explicit vs Implicit 1st order Euler method for Numerical Integration

In this project, we shall take a look at what Adiabatic Flame Temperature is and how to calculate it for various species using the coefficients from NASA's Thermodynamic data and compare it with the results from Cantera in conjunction with Python First of all let us look at what is Adiabatic Flame Temperature, Adiabatic…

In this project, I will discuss the necessity for an implicit numerical scheme and its advantages over an explicit one. For this demonstration, I will use the first order Euler Schemes for Numerical Integration as it is the easiest to use and understand, The first order Euler Numerical scheme is derived from the Taylors…

In this project, I will discuss the concept of Newton Rhapson Method for the Numerical Rootfinding of a Non-Linear Equation, The Newton Rhapson Method for root finding is an iterative Numerical Method of root finding that can never give you the exact root value, it will always give us an approximate root value close to…

In this project, I will be explaining the explicit 1st order explicit Euler method, its usefulness and its limitations. For this example, I have assumed the example of a simple ODE, derived from the motion of a spring-mass system, We know that the ODE depicting this motion is of the form, `m*((d^2x)/dt^2)+c*(dx/dt)+k*x=0`…

This project is an extension of the project shown here, https://projects.skill-lync.com/projects/Solving-a-system-of-ODEs-using-Implicit-Euler-method-86502   In the above-shown project, I have used python to create an Implicit Euler ODE solver for 3 ODEs, If needed to solve for more or less than 3 ODEs, there needs…

In this project, I have discussed and proposed a method to solve a system of stuff ODEs using the first order Implicit Euler method The ODEs I will be solving are in the form of, As it can be observed it is a system of coupled nonlinear ODEs, The solution of this system will explode if we use explicit methods, Hence an…

Assuming we have a spring mass damper system as follows,   we know that the ODE of the system will be of the form,   `m*((d^2x)/dt^2)+c*(dx/dt)+k*x=0` or `m*x''+c*x'+k*x=0` where, `dx/dt=x' and (d^2x)/dt^2=x''`   and if we assume the state variable as `s` then our state space array will be of the of the…

What is Curve Fitting ? Curve fitting is the process of constructing a curve, or mathematical functions, which possess the closest proximity to the real series of data. By curve fitting, we can mathematically construct the functional relationship between the observed dataset and parameter values, etc. It is highly…

`Q_("total")=Q_("work")+Q_("loss")`   `sumQ=M_("air")*H_("air")+M_("air")*H_("air")+M_("products")*H_("products")-Q_("work"+"loss")=0`   `M_("air")*H_("air")+M_("fuel")*H_("fuel")+(M_("air")+M_("fuel"))*H_("products")=Q_("work"+"loss")`   `M_("air")/M_("fuel")*H_("air")+M_("fuel")/M_("fuel")*H_("fuel")+(M_("air")/M_("fuel")+M_("fuel")/M_("fuel"))*H_("products")=Q_("work"+"loss")/M_("fuel")`…

The file parsing project is the last assignment for the MATLAB module for engineers and hence the most challenging. These are some of the common errors encountered while trying to solve the project.   Inconsistency when comparing 2 arrays (element number inconsistency). This error is encountered when students try…

The interface for ZOOM Cloud Meetings for mobile shares a lot of features and is very similar to the full PC / Laptop Edition. For the guide on how to use the ZOOM App for PCs and Laptops please use the link below, https://projects.skill-lync.com/projects/How-to-use-ZOOM--74132   Downloading the Software The software…

This article will be focused on how to use ZOOM app for video conferencing.   STEP 1 Go to the link https://zoom.us/, go to RESOURCES and click the option Download Zoom Client.     After that run ZoomInstaller.exe and install the App.   STEP 2 Upon installing, clicking on the link given to…

Since there has been a lot of confusion regarding changing 2nd order ODEs to 1st order ODEs using state space variables, this project will give a detailed insight on it. This conversion of 2nd order ODEs is required because the ODE23/ODE45 solver in matlab can only accept a 1st degree ODE.    What is a 2nd degree…

What does this ODE mean? First we understood that our ODE defining the motion of a spring mass system was a 2nd order ODE, but what does the eqaution mean? Upon solving the equation by integrating twice (analytical solution) we will get an equation of the form `x(t)` which basically means - the location of the…