Numerical Analyzer

Live at https://numerical-analyzer.netlify.com/

Things Used :

1. Svelte js (Wanted to use it for a loooong time)
2. Chart js (For those charts)
3. Bulma (For CSS and Flex-Box)
4. Math js (For equations and calculations)

What this does :

This web-app solves and graphs any first order ordinary diffrential equation by using 5 numerical methods which are single-stepped
It will also provide you with the base formula and local and global errors along with detailed calculations

This uses svelte, which means once the site is loaded it can work offline :)

Example:

Let's say we take :

• dy/dx = x
• Method = Euler's Forward Method
• Range : 0 < x < 4
• Step size : 0.2
• y(0) = 0

Now if we solve this analytically we have y = x^2/2 and at x = 4, y(x = 4) = 8
Since we also know the analytical solution we'll graph it along with the numerical-solution
Now change the methods to see which gives the correct answer !!!

How can this be used :

• Can be used as a quick checking tool of the numerical-solution in diffrent methods with just few clicks and see their accuracies
• Can be used to visualise the graphs along with the analytical solution so that you can see the error of the method with the analytical solution
• Of course this can be used as a teaching tool

Future of this project

• Due to some time constrains I was able to include 1st order ODE single-step methods only but in future this will support nth order equations in both ODE and PDE and also multi-step processes
• A parallel project would be created for solving simultaneous nth order ODE/PDE which will use this project as a refrence and take the methods from here