Evaluation of Delay Term and Noise Term for Approximate Solution of Stochastic Delay Differential Equation without Interpolation Techniques
The main objective of this study is to tackle the setbacks encountered by many researchers in the evaluations of the delay term and noise term of Stochastic Delay Differential Equation (SDDE) in order to obtain its numerical solution. These setbacks affect the preservation of the accuracy and efficiency of the numerical solution of Stochastic Delay Differential Equation (SDDE) which need to be addressed. Three new mathematical expressions are developed for the evaluations of the delay term and noise term different from the interpolation techniques been used by other researchers which causes setbacks in obtaining and preserving the accuracy of the numerical solutions. These mathematical expressions developed for the evaluations of the delay term and the noise term together with the discrete schemes of Hybrid Extended Block Backward Differentiation Formulae Method (HEBBDFM) are incorporated into some examples of Stochastic Delay Differential Equation (SDDE) for its numerical solutions. The discrete schemes of the method (HEBBDFM) are obtained by continuous formulations of multistep collocation method by matrix inversion approach. The basic properties for the convergence and stability analysis of the method were analyzed and proved satisfactory. The analysis of the numerical results with its comparison and g raphical presentations proved that the method performs better by producing the Least Minimum Absolute Random Errors (LMAREs) at Lesser Computational Processing Unit Time (LCPUT) than other existing methods in terms of accuracy and efficiency using the developed mathematical expressions. Thus, this study recommends the three new mathematical expressions developed for the evaluations of the delay term and noise term different from the interpolation techniques suitable for obtaining better approximate solutions of SDDE.
Keywords: Stochastic delay differential equation, Hybrid Extended Block Backward Differentiation Formulae Method, Delay term, Noise term, Absolute Random Error
Mathematics Subject Classification 2020: 60H10; 91G60; 62-08; 60H40; 60H25.
