Numerical Solution of 1D Heat Equation Using Finite Difference Technique

In this video we solved 1D heat equation using finite difference method. For validation of solution we compared it with analytical solution and showed that ratio of time step divided by square of space step should be less or equal to 0.5, that is what one can expect for explicate method.

[shaami-]

I''m really thankful for all of your videos. very nicely explained everything. please upload more videos

[KM]

Nice work. But I am confused as I think the x and y axis should be swaped with each other and it would also make more sense

[pakarmyisizindabad]

Thanks sir, got same question today in assignment :)

[apuham]

Can you say something about Allen Cheng scheme? And about flux boundary conditions, when derivatives is used?

[wcaleb]

Thank you so much for the video. If possible, could you explain why when s<1/2 the result converges? Is there any mathematical reason behind it? OR could you let me know the mathematical term (name) of this theory?

[mohitpatle]

sir, how to solve 1d transient heat conduction problem having non-dimenssionlized GE. ?

[toufeeqsiddique]

Hi, ,
How to solve the same equation if there's a term infront of Uxx( right hand sight of the equation) like = C^a ?

[WaqarAli-irfc]

Respect sir were you not used boundary conditions in the numerical solution?

[nonato]

Hello teacher! Let's say I had the initial condition UN(x, 0)=25°C with boundary conditions non-homogeneous: UN(L, t)=500°C and UN(0, t)=100°C. How would I define this in the program? If I do:
UN=zeros(nx, nt);
UN(:, 1)=25;
UN(1, :)=100;
UN(end, :)=500;
Would it be correct? I need this for a university program

[altalhi]

Hi, I have a question is the crank nicolson scheme has the same step?

[sofy]

Hello sir i want to descritize équation of mass transfert called solution-diffusion with finite différence method
J=- A∆C this for soluté transport
J=-B(∆p-∆π) this for solvent transport( water)

[gaurav-pskc]

can u solve this equation using implicit method and crank nicolson method

[chamimsttw]

Can you explain for Roshental's equation in matlab sir? thanks

[ljlbarca]

How would we solve the same problem using backward difference instead ?

[shivaraghav]

what to do if we want to do for 2d unsteady?

[Srinivasa-no-eqn-without-god]

Sir it is one dimensional heat equations

[Larayu-ki]

Welcom
Need Fokker Planck equation solution finite difference and how to find errors geometrical and graphical