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Full Description
This book contains an extensive illustration of use of finite difference method in solving the boundary value problem numerically. A wide class of differential equations has been numerically solved in this book. Starting with differential equations of elementary functions like hyperbolic, sine and cosine, we have solved those of special functions like Hermite, Laguerre and Legendre. Those of Airy function, of stationary localised wavepacket, of the quantum mechanical problem of a particle in a 1D box, and the polar equation of motion under gravitational interaction have also been solved. Mathematica 6.0 has been used to solve the system of linear equations that we encountered and to plot the numerical data. Comparison with known analytic solutions showed nearly perfect agreement in every case. On reading this book, readers will become adept in using the method.
Contents
Author biographies
1. A numerical solution of boundary value problem using finite difference method
2. Differential equations of some elementary functions: boundary value problems numerically solved using finite difference method
3. Differential equations of special functions: boundary value problems numerically solved using finite difference method
4. Differential equation of Airy function: boundary value problem numerically solved using finite difference method
5. Differential equation of stationary localised wavepacket: boundary value problem numerically solved using finite difference method
6. Particle in a box: boundary value problem numerically solved used finite difference method
7. Motion under gravitational interaction: boundary value problem numerically solved using finite difference method
8. Concluding remarks
