This article presents a new numerical model with nodes within the interval of eight-step for numerical
simulation of a class of variable coefficient elliptic partial differential equations in the two-dimensional
domain. The method is developed via the principle of collocation and interpolation techniques using Hermite
polynomial as the basis function. The main classical model and its derivatives generated from the continuous
function are then united together to form the required Classical Eight-step Model (CEM). The analysis of the
CEM was investigated and shows that it satisfies the conditions for convergence with an algebraic order of nine.
The CEM is applied to solve the semi-discretized elliptic partial differential equations with a variable coefficient
arising from the discretization of one of their spatial variables. The performance of the CEM was established
with six test problems. The approximate solution generated using CEM is compared with the analytical solution
of the problems and other existing methods in the literature. Numerical illustrations demonstrate that the
method is convergent and highly accurate. The advantages of CEM over other existing methods reveal the
accuracy and efficiency of the CEM as depicted in curves.
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