RESERVOIR NUMERICAL SIMULATION

NUMERICAL SIMULATION

TAYLOR`S SERIE

ROUNDING

Rounding errors

These errors occur because the computers just to hold a finite number of significant figures for a calculation. For example: if you only saved seven significant figures, the computer can store and use p as p = 3 141 592 and generating a rounding error.

ERROR

The numerical errors are generated with the use of approximations to represent mathematical operations and quantity. These include truncation errors, which are from about exact mathematical procedure and the rounding errors that result from about exact numbers.
For both types of errors, the relationship between the exact result and the approximate or true is given by:

Estimated value = true value + error
Numerical error is equal to the difference between the true value and approximate value, ie
Eu = true value - approximate value

ACCURACY AND PRECISION

The accuracy is concerned:
1) the number of significant figures that represent an amount

2) extending from the repeated readings of an instrument that measures some physical property.

For example:

When making some shots in a target shooting accuracy refers to the magnitude of the spread of the bullets.

The precision refers to the approach of a number or measure the true value is supposed to represent.
The inaccuracy (known as bias) is defined as a systematic departure from the truth.

MATHEMATIC MODELATION

A mathematical model is one of the types of scientific models, which employs some form of mathematical formulas to express relationships, substantive propositions of facts, variables, parameters, entities and relationships between variables and / or entities or transactions, to study behavior of complex systems difficult to observe situations in reality.

A modeling process should take the following steps:

1.Identificacion
variable establishing a mathematical notation
2.Leyes
Empirical may apply
3.Planteamiento of equations

NUMERICAL METOHDS

Numerical methods are techniques by which problems can be formulated so as to be adjudicated aritméticas.Aunque operations there are many types of numerical methods all share one common feature, carry out a number of tedious arithmetic