检查具有边界条件的简单偏微分方程 (PDE)： d/dx( x dy/dx ) = x y(0) = y(1) = 0。 两次集成PDE以获得其解决方案。 然后应用边界条件并得到一个矛盾。 边值问题（BVP）无解。 无论如何，请使用分段线性基函数应用有限元方法 (FEM)。 FEM 顺利完成。 没有迹象表明这个问题是无法解决的。 这是因为 FEM 做出限制解空间的假设。 在这个有限的空间内，BVP 确实有一个解决方案。 关键是人们不能盲目地依赖数值技术来得出问题的正确答案。 数值方法需要辅以分析。

时滞系统研究的重要资料 很详细 而且讲解了 线性非线性系统 表达了很多方法Backstepping等等

matlab的欧拉方法代码PDE_Matlab_Code_solution- 作为论文的一部分，我必须用数值​​方法求解PDE。 PDE代表与微生物相关的项目在微观尺度上的梁状结构的位移。 它不是特别适合于解析数学解决方案。 BC取自相关文献，并采用Euler前向有限差​​分法。 PDE读取u_t =（beta / 4）*（s ^ 2 -1） u_ss-（1 / eta） （u_ssss）。

Time dependent problems frequently pose challenges in areas of science and engineering dealing with numerical analysis, scientific computation, mathematical models, and most importantly—numerical experiments intended to analyze physical behavior and test design. Time Dependent Problems and Difference Methods addresses these various industrial considerations in a pragmatic and detailed manner, giving special attention to time dependent problems in its coverage of the derivation and analysis of numerical methods for computational approximations to Partial Differential Equations (PDEs). The book is written in two parts. Part I discusses problems with periodic solutions; Part II proceeds to discuss initial boundary value problems for partial differential equations and numerical methods for them. The problems with periodic solutions have been chosen because they allow the application of Fourier analysis without the complication that arises from the infinite domain for the corresponding Cauchy problem. Furthermore, the analysis of periodic problems provides necessary conditions when constructing methods for initial boundary value problems. Much of the material included in Part II appears for the first time in this book. The authors draw on their own interests and combined extensive experience in applied mathematics and computer science to bring about this practical and useful guide. They provide complete discussions of the pertinent theorems and back them up with examples and illustrations. For physical scientists, engineers, or anyone who uses numerical experiments to test designs or to predict and investigate physical phenomena, this invaluable guide is destined to become a constant companion. Time Dependent Problems and Difference Methods is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations.

FOURIER NEURAL OPERATOR FOR parametric pde

二阶双曲型偏微分方程的二阶精度隐格式，一阶精度显格式以及改进的二阶精度显格式

林石算子PDE,用于图像处理，经验证过了，效果非常好

有关算子半群方法的很经典的一部国外专著,书中语言简练易懂，适合低年级的pde研究生，当然，也是pde研究者的一部不错的参考书

A. Tveito, R. Winther - Introduction to Partial Differential Equations - A Computational Approach

该程序用于模拟微波加热一杯水。 对于笛卡尔坐标系和圆柱坐标系均获得了解，并将结果与​​一维模型和集总电容模型进行了比较。 结果表明，使用这些简化模型会导致大量错误。