NUMERICAL SOLUTION OF FIRST AND SECOND ORDER DIFFERENTIAL EQUATIONS USING THE TAU METHOD WITH AN ESTIMATION OF THE ERROR (FUDMA JOURNAL OF SCIENCES, 2025)
The Subject of Numerical methods is an important aspect of ordinary differential equations. It is useful in providing solutions to a wide variety of complex differential equations arising from engineering, physical and biological sciences, health and other allied disciplines which are difficult to tackle by exact methods. Numerical approximations of differential equations of one and higher order have been provided using Euler Method, Tau Method, Runge-Kutta Method, Adams-Bashforth Method, Milne Simpson predictor-corrector Method, Adams-Moulton linear multistep method and a host of others. In this paper, we discussed the application of tau method for solving first and second order initial value problems of ordinary differential equations. Numerical examples are given for the sake of illustration of the method. To validate the accuracy of the method, we compare the approximate solutions obtained with exact solutions. By estimating the error, it is observed that the error decreases as the order of Tau approximations increases. This showed the performance and computational efficiencies of tau method.
Keywords: Tau method; Numerical Solution; Differential Equation; Error; Accuracy