1 Finite difference formulas 1.1 Problem definition We have seen that one of the necessary ingredients in devising finite differe

Finite Difference Problem Definition Formulas

Poisson Equation in 1D Model Problem Boundary Value Problem(BVP) Wra(ac)= f(a) N1 x∈(0,1),w(0)=(1)=0,f∈C0N2 Describes many simple physical phen

1 Model problem 1.1 Poisson Equation in 1D Boundary Value Problem(BVP) (x)=∫(x) (0,1),u(0)=(1)=0,f Describes many simple physical phenomena(e.g) Deformation of an elastic bar Deformation of a string under tension Temperature distribution in a bar The Poisson equation in one dimension is in fact an ordinary differ tion. When dealing with ordinary differential equations we Poisson equation will be used here to illastrate numerical techniques for elliptic PDE's in multi-dimensions. Other techniques specialized for ordinary differen tial equations could be used if we were only interested in the one dimension

Course Outline Overview of pdes(1) o Finite differences methods(6) Finite volume methods(3) Finite element methods(7) Boundary integral methods(6)

Despite its apparent simplicity this equation appears in a wide range of dis m heat 7 to financial er we will make extensive use of this equation, and several of the limiting cases contained therein, to illustrate the numerical techniques that will be presented

An ICBM with a range of 6500 miles has a stagnation temperature of 12,000 ºF, 2000 ºF hotter than the surface of the sun Calculations showed that the optimum design for structural strength, resistance to heating, and free flight stability was a long, needle nosed reentry body

Outline Purpose of thermal control systems Review of heat transfer fundamentals Space system thermal analysis Equations Models Analysis programs

Overview Ground Systems Support the space segment Command and Control Monitor spacecraft health Track Calculate spacecraft attitude

Satellite CommunicationsArchitecture Identify Requirements Specify Architectures Determine Link Data Rates Design & Size each link Document your rationale