Computational methods Chapter one Number system and Numerical Error Analysis Introduction Computational methods Computational methods (numerical analysis) • a tool used to solve Physical problems by writing computer programs • Why numerical? • Numerical solution can be obtained even when no analytical solution is found • The analytical solution is space and time consuming • Numerical Vs Analytical • Numerical uses numerical approximation to solve problems • Analytical uses methods to find an exact solution for a problem Computational method uses scientific computing Representation of Integers and Fractions Number Systems Number system Number system … Number system … Representation of Integers and Fractions Base conversion Base Conversion Base conversion … Base conversion … Base conversion … Base conversion … Base conversion … Base conversion … Base Conversion… Base Conversion… Representation of Integers and Fractions Number representation in computers IEEE standard IEEE standard .. IEEE standard … Numerical errors Chopping and rounding Chopping and rounding Chopping and Rounding … Numerical Errors Numerical errors… Numerical Errors .. Discretization error Example Numerical Errors .. Discretization error Example … Numerical Errors .. Discretization error Example … Numerical errors… Numerical errors … Discretization and round off effects Numerical errors … Discretization and round off effects .. Numerical errors … Floating point arithmetic Numerical Errors … Numerical Errors … Numerical Errors …. Round off Error accumulation Numerical Errors … Numerical Errors … Numerical Errors … Numerical Errors … Numerical Errors … Numerical Errors … Algorithm Properties Problem conditioning and algorithm stablity Numerical Errors … Numerical Errors … Error accumulation .. Numerical Errors … Error accumulation ..
