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Aziz, A.K., French, D.A., Jensen, S., Kellogg, R.B.: Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem. Math. Model. Numer. Anal. 33(5), 895–922 (1999)
Beals, R.: On an equation of mixed type from electron scattering theory. J. Math. Anal. Appl. 58, 32–45 (1977)
Beals, R.: Indefinite Sturm-Liouville problems and half-range completeness. J. Differ. Equ. 56, 391–407 (1985)
Davis, T.A.: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia (2006)
Degond, P., Mas-Gallic, S.: Existence of solutions and diffusion approximation for a model Fokker-Planck equation. Transport Theory Stat Phys 16, 589–636 (1987)
Fisch, N.J., Kruskal, M.D.: Separating variables in two-way diffusion equations. J. Math. Phys. 21, 740–750 (1980)
Franklin, J.N., Rodemich, E.R.: Numerical analysis of an elliptic-parabolic partial differential equation. SIAM J. Numer. Anal. 5(4), 680–716 (1968)
Han, H., Yin, D.: A non-overlap domain decomposition method for the forward-backward heat equation. J. Comput. Appl. Math. 159(1), 35–44 (2003)
Kim, A.D., Tranquilli, P.: Numerical solution of the Fokker-Planck equation with variable coefficients. J. Quant. Spectrosc. Radiat. Transf. 109(5), 727–740 (2008)
Klaus, M., van der Mee, C.V.M., Protopopescu, V.: Half-range solutions of indefinite Sturm-Liouville problems. J. Funct. Anal. 70, 254–288 (1987)
López Pouso, Ó., Jumaniyazov, N.: Numerical experiments with the Fokker-Planck equation in 1D slab geometry. J. Comput. Theor. Transport 45(3), 184–201 (2016)
Sheng, Q., Han, W.: Well-posedness of the Fokker-Planck equation in a scattering process. J. Math. Anal. Appl. 406, 531–536 (2013)
Stein, D., Bernstein, I.B.: Boundary value problem involving a simple Fokker-Planck equation. Phys. Fluids 19, 811–814 (1976)
Sun, J.: Numerical schemes for the forward-backward heat equation. Int. J. Comput. Math. 87(3), 552–564 (2010)
Vanaja, V.: Numerical solution of a simple Fokker-Planck equation. Appl. Numer. Math. 9(6), 533–540 (1992)
Vanaja, V., Kellogg, R.B.: Iterative methods for a forward-backward heat equation. SIAM J. Numer. Anal. 27(3), 622–635 (1990)