Numerical Solutions of Boundary Value Problems with Finite Difference Method
Description
Containing an extensive illustration of the use of finite difference method in solving boundary value problems numerically, a wide class of differential equations have been numerically solved in this book. Starting with differential equations of elementary functions like hyperbolic, sine and cosine, special functions such as Hermite, Laguerre and Legendre are solved. Airy function, stationary localised wavepacket, the quantum mechanical problem of the particle in a 1D box and polar equation of motion under gravitational interaction are also explored.
Aimed at ensuring readers become adept in using the method, Mathematica 6.0 is used to solve systems of linear equations, and to plot the numerical data, and comparison with known analytic solutions showed nearly perfect agreement in every case.
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Content
Chapter I Numerical Solution of Boundary Value Problem Using Finite Difference Method 1.1 Statement of the problem 1.2 Approximation to derivatives 1.3 The finite difference method
Chapter II Differential Equations of Some Elementary Functions: Boundary Value Problems Numerically Solved Using Finite Difference Method 2.1 The differential equation for hyperbolic function 2.2 The differential equation for Cosine function 2.3 The differential equation for Sine function
Chapter III Differential Equations of Special Functions: Boundary Value Problems Numerically Solved Using Finite Difference Method 3.1 The Hermite differential equation 3.1.1 Hermite polynomial H3(x) 3.2 The Laguerre differential equation 3.2.1 Laguerre polynomial L3(x) 3.3 The Legendre differential equation 3.3.1 Legendre polynomial P3(x)
Chapter IV Differential Equation of Airy Function: Boundary Value Problem Numerically Solved Using Finite Difference Method 4.1 The differential equation for Airy function
Chapter V Differential Equation of Stationary Localised Wavepacket: Boundary Value Problem Numerically Solved Using Finite Difference Method 5.1 Differential equation for stationary localised wavepacket
Chapter VI Particle in a Box: Boundary Value Problem Numerically Solved Using Finite Difference Method 6.1 The Quantum Mechanical problem of particle in a onedimensional Box
Chapter VII Motion under gravitational interaction: Boundary Value Problem Numerically Solved Using Finite Difference Method 7.1 Motion under gravitational interaction Concluding remarks References
