Partial Differential Equations With Fourier Ser... -
). The spatial ODE is typically an eigenvalue problem (e.g.,
u(x,t)=∑n=1∞AnXn(x)Tn(t)u open paren x comma t close paren equals sum from n equals 1 to infinity of cap A sub n cap X sub n open paren x close paren cap T sub n open paren t close paren Use the initial condition (e.g., ) to determine the coefficients Ancap A sub n Partial Differential Equations with Fourier Ser...
An=2L∫0Lf(x)sin(nπxL)dxcap A sub n equals the fraction with numerator 2 and denominator cap L end-fraction integral from 0 to cap L of f of x sine open paren the fraction with numerator n pi x and denominator cap L end-fraction close paren d x Partial Differential Equations with Fourier Ser...
Since the PDE is linear, any linear combination of your product solutions is also a solution. Express the general solution as an infinite sum : Partial Differential Equations with Fourier Ser...
so when we get to that point I we'll explain all of these things one after the other but here I'm just trying to give an overview. YouTube·Emmanuel Jesuyon Dansu Heat Equation and Fourier Series