A pseudo-spectral solution of 2-parameter Bratu's equation
A simple pseudo-spectral (collocation type) method is used to study the boundary value problem: \(\frac{\partial^ 2u}{\partial x^ 2}+\frac{\partial^ 2u}{\partial y^ 2}+\lambda \exp (\frac{u}{1+\epsilon u})=0,\) \(0\leq | x|\), \(| y| \leq 1\), \(u(\pm 1,y)=u(x,\pm 1)\) where \(\lambda\),\(\epsilon\) are parameters. The resulting nonlinear set of algebraic equations is solved using a constant-arc type continuation method. The present algorithm is capable of successfully obtaining the various turning points in both \(\lambda\)- u(0,0) curves as well as \(\epsilon\)-u(0,0) curves.
scientific article; zbMATH DE number 4174269