Numerical Derivatives by Symbolic Tools in MATLAB

Abstract: Numerical approaches of ordinary differential equations (ODEs) usually require Jacobian evaluations and sometimes higher order derivatives of system of equations. The evaluation of these numerical derivatives can either use algebraic derivation or by the computer algebra system (CAS), such as MAPLE V, but these derivations may either cause debugging difficulty in programming or memory swell in computation. Finite difference formulas including forward difference, central difference, and backward difference are used to derive the Jacobian with different degree of accuracy. Symbolic evaluation capability of MATLAB is used to enhance fast derivation of numerical derivatives given in this paper. The accuracy of these numerical derivatives shows that the evaluation by symbolic computation from MATLAB is possible to be equipped into a numerical scheme of ordinary equations