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
In the contractual agreement of an option,the value at which the contract is settled is one of the pertinent factors to consider and the problem is to compute and come up with a model that encapsulates the current pri...In the contractual agreement of an option,the value at which the contract is settled is one of the pertinent factors to consider and the problem is to compute and come up with a model that encapsulates the current price of an asset,strike price of the option,asset’s volatility,maturity time and risk-free interest rate and the Black-Scholes model was the first model with all of these factors and this paper presents the algorithms to approximate solutions of Black Scholes financial model using the Adomian Decomposition and Power Series collocation methods,and presents comparative findings of the exact solution of Black Scholes financial model with approximate solutions from the Adomian Decomposition and Power Series collocation methods.The Adomian Decomposition method gives a better and more accurate result to the Power Series Collocation method for solving the Black Scholes financial model.Both methods are therefore efficient and agree with the exact solution of the model.展开更多
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.
文摘In the contractual agreement of an option,the value at which the contract is settled is one of the pertinent factors to consider and the problem is to compute and come up with a model that encapsulates the current price of an asset,strike price of the option,asset’s volatility,maturity time and risk-free interest rate and the Black-Scholes model was the first model with all of these factors and this paper presents the algorithms to approximate solutions of Black Scholes financial model using the Adomian Decomposition and Power Series collocation methods,and presents comparative findings of the exact solution of Black Scholes financial model with approximate solutions from the Adomian Decomposition and Power Series collocation methods.The Adomian Decomposition method gives a better and more accurate result to the Power Series Collocation method for solving the Black Scholes financial model.Both methods are therefore efficient and agree with the exact solution of the model.
