金属材料位错密度演化的数学问题
On mathematical aspects of evolution of dislocation density in metallic materials
摘要：
本文讨论了金属材料中位错密度演化的延迟微分方程的求解问题。硬化，恢复和再结晶特征的位错种群的演变提供了该模型的基本方程。最后一项将常微分方程（ODE）转化为具有强（一般为Hölder）非线性的延迟微分方程（DDE）。我们证明了显式欧拉法的误差界，假设右手边的功能是Hölder连续和单调的，使我们能够比较我们的模型（例如龙格库塔）中的其他数值方法的精度，特别是当显式公式的解决方案是未知的。最后，我们在实际工业过程的模拟测试上述结果。
英文摘要：
This paper deals with the solution of delay differential equations describing evolution of dislocation density in metallic materials. Hardening, restoration, and recrystallization characterizing the evolution of dislocation populations provide the essential equation of the model. The last term transforms ordinary differential equation (ODE) into delay differential equation (DDE) with strong (in general, Hölder) nonlinearity. We prove upper error bounds for the explicit Euler method, under the assumption that the right-hand side function is Hölder continuous and monotone which allows us to compare accuracy of other numerical methods in our model (e.g. Runge-Kutta), in particular when explicit formulas for solutions are not known. Finally, we test the above results in simulations of real industrial process.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
