Software for Error Controlled Numerical Solution of Boundary Value Ordinary Differential Equations and Parabolic Partial Differential Equations

与理论和实验科学一样，计算建模现在被视为科学探究的第三个基本分支。在化学、物理、生物和金融等领域产生的大多数计算模型都涉及到复杂的微分方程组(DES)，这些微分方程组的近似解是通过使用复杂的数值软件获得的。由于数值解是近似的，因此软件还必须评估计算解的质量。两种流行的评估类型是整体误差(近似解和精确解之间的差异)和缺陷(数值解未能满足方程的程度)。高质量的软件将调整计算，以便可以有效地获得数值解，并且使得对全局误差或缺陷的估计满足用户提供的容差。

Along with theoretical and experimental science, computational modeling is now viewed as a third fundamental branch of scientific inquiry. A majority of computational models, arising in such areas as chemistry, physics, biology, and finance, involve complex systems of differential equations (DEs), for which approximate solutions are obtained through the use of sophisticated numerical software. Because the numerical solutions are approximate, it is essential that the software also assess the quality of the computed solution. Two popular types of assessment are the global error (the difference between the approximate and exact solutions) and the defect (the amount by which the numerical solution fails to satisfy the equations). Good quality software will adapt a computation so that the numerical solution can be obtained efficiently and so that an estimate of the global error or defect satisfies a user-provided tolerance.