Parameter Estimation of Potentials which are Solutions of some Second-Order Ordinary Differential Equation - Surulere, S. A.; Malange, T.; Shatalov, M. Y.; Mkolesia, A. C. (Discontinuity, Nonlinearity, and Complexity, 2026)
The parameter estimation of interatomic potentials are considered as a solution of some second order ordinary differential equation. The developed method for the multiple goal function approach can be applied to a wide range of transcendental nonlinear problems. The parameter estimation of several interatomic potentials in classical functional forms are estimated using the objective least squares function method. Potentials such as Lennard-Jones, Classical Rydberg, Classical, Generalized Morse and Biswas-Hamann potential were each considered. Two new interatomic potentials, Modified Generalized Morse and Modified Lennard-Jones potential are proposed in this text. Numerical estimates were obtained using gold atom for numerical simulation in MathCad® software while the potential energy curves are constructed and reconstructed in Mathematica®. The estimated parameters gave good fit to experimental data sets of gold atom as the error plots of the potential energy curves are small. The values obtained for the goal function also shows that the approximated parameters values are good approximations.