Nawaz, Y., et al.: A New Class of A-Stable Numerical Techniques for ... THERMAL SCIENCE: Year 2021, Vol. 25, No. 3A, pp. 1665-1675 1665 A NEW CLASS OF A-STABLE NUMERICAL TECHNIQUES FOR ORDINARY DIFFERENTIAL EQUATIONS Application to Boundary-Layer Flow by Yasir NAWAZ * and Muhammad Shoaib ARIF * Stochastic Analysis and Optimization Research Group, Department of Mathematics, Air University, PAF Complex E-9, Islamabad, Pakistan Original scientific paper https://doi.org/10.2298/TSCI190926097N The present attempt is made to propose a new class of numerical techniques for fnding numerical solutions of ODE. The proposed numerical techniques are based on interpolation of a polynomial. Currently constructed numerical techniques use the additional information(s) of derivative(s) on particular grid point(s). The ad- vantage of the presently proposed numerical techniques is that these techniques are implemented in one step and can provide highly accurate solution and can be constructed on fewer amounts of grid points but has the disadvantage of fnding derivative(s). It is to be noted that the high order techniques can be constructed us- ing just two grid points. Presently proposed fourth order technique is A-stable but not L-stable. The order and maximum absolute error are found for a fourth order technique. The fourth order technique is employed to solve the Darcy-Forchheimer fuid-fow problem which is transformed further to a third-order non-linear bound- ary value problem on the semi-infnite domain. Key words: interpolation, Darch-Forchheimer fow, A-stable, derivative(s), maximum absolute error Introduction Numerical methods can be considered to apply when some physical phenomena are expressed in mathematical form. Also, some analytical methods have been considered to solve the diferential equations that arise from physical phenomena(s). The main beneft of using nu- merical methods is their speed of solving the problem when compared with analytical methods. Since the analytical methods use algebra in the computations, so due to this fact, the analytical methods may take more time to solve the problem(s). Some numerical methods are those kinds of methods that provide high order numerical solution, and some can be used to reduce oscil- lations in the solution. Also, one class of numerical methods is Runge-Kutta methods which may provide high order solution but these methods are applied in diferent steps. Some of the presently constructed numerical methods can provide high order solution and can be construct- ed on just two grid points. Jones [1] applied fnite diference method for solving Navier stokes equations and sea breeze model, and applied fnite diference method that was developed in their/his previous work for the improvement of accuracy and computational efciency. In [2], the comparison of homotopy perturbation method and the fnite diference method is given and proved that the * Corresponding author, e-mail: 171438@students.au.edu.pk; shoaib.arif@mail.au.edu.pk