Geodesic
The method of lines in application to some two-dimensional nonlinear parabolic equations
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 132-142

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We consider the first mixed problem for nonlinear parabolic equation. Assuming that the exact solution of the problem is $u(t,x,y)\in C^{4,0}(Q)$, $Q=\{(x,y)\in\Omega,0\leq t\leq T\}$ we construct a scheme of the method of straight lines of accuracy $O(h^2)$ for the cases when $\Omega$ is a rectangle or a trapezoid. 
@article{ZNSL_1987_159_a13,
     author = {A. P. Kubanskaya},
     title = {The method of lines in application to some two-dimensional nonlinear parabolic equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {132--142},
     publisher = {mathdoc},
     volume = {159},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_159_a13/}
}
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A. P. Kubanskaya. The method of lines in application to some two-dimensional nonlinear parabolic equations. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 132-142. http://geodesic.mathdoc.fr/item/ZNSL_1987_159_a13/