In this paper the Black Scholes differential equation is transformed into a parabolic heat equation by appropriate change in variables. The transformed equation is semi-discretized by the Method of Lines (MOL). The ev...In this paper the Black Scholes differential equation is transformed into a parabolic heat equation by appropriate change in variables. The transformed equation is semi-discretized by the Method of Lines (MOL). The evolving system of ordinary differential equations (ODEs) is integrated numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10–10.展开更多
In this paper, the one-dimensional time dependent Schr?dinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evo...In this paper, the one-dimensional time dependent Schr?dinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff Ordinary Differential Equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10?4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.展开更多
文摘In this paper the Black Scholes differential equation is transformed into a parabolic heat equation by appropriate change in variables. The transformed equation is semi-discretized by the Method of Lines (MOL). The evolving system of ordinary differential equations (ODEs) is integrated numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10–10.
文摘In this paper, the one-dimensional time dependent Schr?dinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff Ordinary Differential Equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10?4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.
