原创 Comparation of liquid film drains down insideand outside the straw

問題描述 一個最近在看Panton的《Incompressible Fluid Mechanic》想到的問題:水流順着吸管流下是沿着外壁流下得快還是內壁流下得快。 A liquid film drains down the out

原创 Poisson Equation on a Square Domain, Dirichlet Boundary Conditions

Introduction to the problem Consider the boundary-value problem ∂2u∂x2+∂2u∂y2=x+y\frac{{\partial}^{2}u}{{\partial}x

原创 Dirichlet kernel and Fejer Kernel and their convergence

Dirichlet kernel and Fejer Kernel Considered the convergence of Fourier series (or more precisely, the N-th sum SNf

原创 Analytical and Numerical solution of a Boundary Value Problem

Introduction to the problem t2x′′(t)+3tx′(t)+x(t)=t(t>1)t^2x{''}(t)+3tx{'}(t)+x(t) = t \qquad (t>1)t2x′′(t)+3tx′(t)

原创 Comparation of numerical and analytical solution of 1-D Heat Equation

Introduction 1-d Linear heat Equation: ∂u∂t=c∂2u∂x2 \frac{\partial u}{\partial t} = c \frac{\partial^2 u}{\partial

原创 1-D 2nd order Convection-Diffusion equation

Introduction to the problem 1-D 2nd order Convection-Diffusion equation ∂u∂t+u∂u∂x=υ∂2u∂x2 \frac{\partial u}{\parti

原创 Heat kernel and its properties

Heat kernel 什麼是heat kernel呢?結果令人震驚! Hi,大家好,這裏是給阿姨倒一杯卡布奇諾。今天,我們來說一下在1-D 2nd order Convection-Diffusion equation中anal