In this work, we will study a numerical method that allows finding an approximation of the exact solution for a in-situ combustion model using the nonlinear mixed complementary method, which is a variation of the Newtons method for solving nonlinear systems based on an implicit finite difference scheme and a nonlinear algorithm mixed complementarity, FDA-MNCP. The method has the advantage of provide a global convergence in relation to the finite difference method and method of Newton that only has local convergence. The theory is applied to model in-situ combustion, which can be rewritten in the form of mixed complementarity also we do a comparison with the FDA-NCP method

This study investigates conditions under which information dimension provides an upper bound for Hausdorff dimension using Shannon entropy and box occupancy. We establish a sufficient entropic condition and introduce the asymptotic entropic quotient, which measures the proportion of maximal entropy retained across scales. Its complement quantifies entropy loss, while its reciprocal defines an entropic correction factor. Cantor-type examples show that the quotient distinguishes distributions sharing the same geometric support. For finite samples, we justify a constrained least-squares estimator and develop a multi-criteria procedure for selecting the principal scaling window. The framework is applied to the Hénon, Lorenz, Ikeda, Rössler, and Chua double-scroll attractors, with sensitivity analyses for sample size and window selection. Estimated entropy losses range from 3.69% to 8.35%, and the entropic quotients remain stable across the tested conditions. The correction improves agreement with the reported Hausdorff dimension for Lorenz. For Hénon, it does not improve that agreement, although both estimates remain compatible with reported fractal dimensions. Results for Ikeda, Rössler, and Chua are consistent in scale with reported dimensions. Overall, the quotient provides distributional information beyond box occupancy and supports a finite-scale interpretation of entropy loss and its associated dimensional correction.

In this work, we study a numerical method to approximate the exact solution of a simple in situ combustion model. To achieve this, we use the mixed nonlinear complementarity method (MNCP), a variation of the Newton method for solving nonlinear systems, incorporating a single Hadamard product in its formulation. The method is based on an implicit finite difference scheme and a mixed nonlinear complementarity algorithm (FDA-MNCP). One of its main advantages is that it ensures global convergence, unlike the finite difference method and the Newton method, which only guarantee local convergence. We apply this theory to an in situ combustion model, reformulating it in terms of mixed complementarity. Additionally, we compare it with the FDA-NCP method, demonstrating that the FDA-MNCP is computationally more efficient when the spatial discretization is refined.