A SPLITTING FLUX LIMITER FINITE DIFFERENCE SCHEME FOR THE NONLINEAR BLACK-SCHOLES EQUATION

We present and analyze a splitting numerical scheme for nonlinear models of mathematical finance. Each problem is split into two parts: a hyperbolic equation solved numerically by using a flux limiter technique, and a parabolic equation computed by an implicitexplicit finite difference scheme. We show that the presented splitting numerical schemes are positivity preserving and monotone. The convexity of the numerical solutions are studied. Numerical results are also discussed