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Table of Contents

(Homework problems below)

Basic Routines

• Machine Epsilon
• Absolute and Relative Error
• Logistic Differential Equation
• Second Order Linear DE with Constant Coefficients

Norms

• Vector P Norm
• Vector Infinity Norm
• Matrix One Norm
• Matrix Infinity Norm

Linear Solvers

• Thomas Algorithm
• Jacobi Iteration
• Conjugate Gradient
• Linear Solver by LU Factorization
  • Lu Factorization
  • Forward Substitution
  • Back Substitution

Eigenvalue Methods

• Power Method Iteration for Largest Eigenvalue
• Inverse Power Method for Smallest Eigenvalue
• Power Method Iteration for Solving 2nd Order FD Elliptic ODE
• Inverse Power Method for Solving 2nd Order FD Elliptic ODE

Elliptic Problems

• Finite Difference Coefficients
• Initialize Elliptic ODE
• Solve Elliptic ODE
• Solve Laplace Equation with 5-point Stencil
  • Generate 5-point Stencil
  • Generate Mesh
  • Initialize B for Mesh

First Order IVPs

• Explicit Euler
• Implicit Euler
  • Newton’s Method
• Runge Kutta order 2
• Runge Kutta order 4
• Predicticor Corrector - Adams Bashforth / Adams Moulton

Parabolic Problems

• Upwinding
• Lax-Wendorff Method
• Warming and Beam Method

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Homework 1

due: 25 January 2018

Problem	Software Manual
Problem 2-3.	Machine Epsilon
Problem 4.	Absolute and Relative Error
Problem 6.	Logistic Differential Equation
Problem 7.	Second Order Linear DE with Constant Coefficients

Homework 2

due: 8 February 2018

Problem	Software Manual
Problem 1-2.	Finite Difference Coefficients
Problem 3.	Initialize Elliptic ODE
Problem 4.	Thomas Algorithm
Problem 5.	Linear Solver by LU Factorization
	Lu Factorization
	Forward Substitution
	Back Substitution
Problem 6.	Jacobi Iteration
Problem 8.	Solve Elliptic ODE
	Vector P Norm
	Vector Infinity Norm

Homework 3

due: 1 March 2018

Problem	Software Manual
Problem 1.	Matrix One Norm
	Matrix Infinity Norm
Problem 2.	Power Method Iteration for Largest Eigenvalue
	Inverse Power Method for Smallest Eigenvalue
Problem 3.	Power Method Iteration for Solving 2nd Order FD Elliptic ODE
Problem 4.	Inverse Power Method for Solving 2nd Order FD Elliptic ODE
Problem 5.	Solve Laplace Equation with 5-point Stencil
	Generate 5-point Stencil
	Generate Mesh
	Initialize B for Mesh
Problem 6.	Solve Laplace Equation with 9-point Stencil
	Generate 9-point Stencil

Homework 4

due: 22 March 2018

Problem	Software Manual
Problem 1.	Gauss-Seidel
Problem 2.	Conjugate Gradient
Problem 3.	Application of Conjugate Gradient
Problem 4.	Explicit Euler

Homework 5

due: 3 April 2018

Problem	Software Manual
Problem 1.	First Order IVP Test
	Logistic Model Test
Problem 2.	IVP via Explicit Euler Test
Problem 3.	Implicit Euler
	Newton’s Method
Problem 4.	Runge Kutta order 2
	Runge Kutta order 4
Problem 5.	Adam’s Bashford
Problem 6.	Summary of Iterative Methods

Homework 6

due: 24 April 2018

Problem	Software Manual
Write up	Experiments 7.1, 7.2, 7.4

Homework 7

due: 5 May 2018

Problem	Software Manual
Problem 1.	Heat Equation - Explicit Euler
Problem 2.	Heat Equation - Implicit Euler
Problem 4.	Heat Equation - Predictor Corrector
Problem 5.	Heat Equation - Runge Kutta Order 4

Homework 8

due: 5 May 2018

Problem	Software Manual
Problem 1.1	Upwinding
Problem 1.2	Lax-Wendorff Method
Problem 1.3	Warming and Beam Method
Problem 2.1	vonNeuman Stability Analysis Lax Wendroff
Problem 2.2	vonNeuman Stability Analysis Warming and Beam