NUMERICAL METHOD (GALAT)

Numerical methods are techniques that are used to formulate the mathematical problem to be solved by arithmetic operations. With computers it can handle complex problem and involves extensive calculation, for example, to solve the problem not the solution of a linear equation, a large system of equations, and other matters included in the technical and social. Problems that are difficult or impossible solved by analytically can solved by numerical methods.

Analytical method is a method of resolving mathematical model with algebraic formulas that prevalent. Numerical method is a technique used to formulate the mathematical problem that can solved with arithmetic operations (+, -, x, and :)

The material that will bi discussed in this lecture in this subject begins with a discussion of the importance of studying numerical methods, mathematical models for engineering problems, programming and software averview that can be used to solve numerical problems, values and error (galat) approach, the description oftaylor series to determine the value of function, differential, interpolation, determining root non-linear equations, solving equation system by using method: elimination, Gaus elimination, Gaus Jourdan elimination, LU decomposition, nemerical integration, second-degree differential equations, Runge Kutta method, applications using numerical methods.

The difference numerical, method with is analytic method solutions. solution by numerical methods is always a number, while usually in the form of analytic functions that must analyzed and then generate numbers. while exact solution solution is in analytic solution (error = 0), while in numerical, the solution in the form of approach so there is a difference called errors (Galat).

Advantages analytical method and numerical methods. Advantages Analytical method is the value obtained is true or exact solution value. while advantages of numerical methods is always can obtain solution with computers, fast calculations and the results can be made as close to the true value and display the results of calculations can be in simulate

Disadvantages of Analytical Methods and numerical methods. Disadvantages  analytical method is need a lot of time, energy and thoughts, and sometimes do not find a solution. Disadvantage numerical methods is the value obtained is approximations and not exact solution values ​​and without the help of calculators, the calculation is generally long and repetitive.

There are many variaty  package of computer programs (eg exel, maple, matlab, or other package programs) that available and trafficked so easy to operate include numerical methods. Thereby, solving the problem simply adjust to the characteristics of the program package with algorithm that are used in solving the problem.

Analytic method is also called true method because it provides a true (exact solution ) or a real , ie a solution that has galat (galat) equal to zero. Galat related by how close approximation to the solution of exact . The smaller the galat, the closer the approximation to the exact , or in other words, the more rigorous numerical solution that obtained.