Inverse Problem Model of Partial Differential Equation of Formation Damage and Research of its Numerical Algorithm 地层伤害偏微分方程反问题模型及计算方法研究
It is proved that equilibrium solutions of this differential system are solutions to the complementarity problem and a numerical algorithm is given based on the numerical integration of the system of ordinary differential equations. 在一定条件下,证明了微分方程系统的平衡点是非线性互补问题的解并且基于一般微分方程系统的数值积分建立了一个数值算法。
Therefore, the differential equations theory and practical numerical methods research become hot spots in mathematical algorithm and engineering academic research. 因此,微分方程数值方法理论和实用算法的研究成为数学和工程学术领域研究的热点问题。
To deal with the strong singular integral-high order differential governing equations in the single-layer model, the author developed a synthetical numerical algorithm which includes numerical integral algorithm, finite difference algorithm and the method to weaken the strong singular kernels in the integrals. 为了能够处理单层模型中的强奇异积分-高阶微分方程组,我们发展了一种包括了数值积分方法、有限差分方法及弱化强奇异方法的强奇异积分-微分方程组融合数值解法。
A linearized modifying algorithm based on multi-resolution analysis and wavelet - Galerkin method is proposed, which can be used to improve the precision of the approximate solution of nonlinear partial differential equations. Error estimates and the numerical examples indicate the effectiveness of the proposed algorithm. 基于多尺度分析和Galerkin方法,提出了一类改进非线性偏微分方程的已知逼近解精度的线性化修正方法.通过误差分析和数值例子说明了方法的有效性。