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

翻译：本研究探讨一种利用非线性混合互补方法求解燃烧原位模型精确解近似值的数值方法。该方法为牛顿法的一种变体，基于隐式有限差分格式和非线性混合互补算法（FDA-MNCP）来求解非线性系统。相较于仅具备局部收敛性的有限差分法和牛顿法，本方法具有全局收敛的优势。理论部分应用于燃烧原位模型的求解，该模型可改写为混合互补形式。研究同时与FDA-NCP方法进行了对比分析。