NUMERICAL SOLUTION Meaning and
Definition
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A numerical solution, also referred to as a numerical approximation, is a method to obtain an approximate solution to a mathematical problem, particularly when an exact solution cannot be determined. It involves using computation and algorithms to approximate solutions to equations or problems that involve complex mathematical techniques and calculations.
Numerical solutions are commonly used in various fields, including physics, engineering, computer science, finance, and other sciences. When faced with mathematical problems that cannot be solved analytically or when the manual calculations are not feasible, numerical methods offer efficient and accurate alternatives.
The process of obtaining a numerical solution generally involves breaking down the problem into smaller, manageable parts and performing calculations using numerical algorithms. This can include iterative methods, interpolation, differentiation, integration, optimization, and more. These techniques make use of numerical approximations, such as finite differences, numerical integration, finite element methods, and others.
The reliability and accuracy of numerical solutions depend on multiple factors, including the complexity of the problem, the precision of calculations, the size of the dataset, and the chosen algorithm. It is important to note that numerical solutions are not always completely accurate, but they are often close enough and provide valuable insights when an exact solution is not available.
In summary, a numerical solution is a computational method used to obtain an approximate solution to a mathematical problem, allowing researchers and professionals to tackle complex calculations and equations efficiently and effectively.
Etymology of NUMERICAL SOLUTION
The word "numerical" comes from the Latin word "numerus", meaning "number". It is derived from the Proto-Indo-European root "*nem-" which also gave rise to words like "number", "numeral", and "numerate". The term "numerical" is used to describe anything related to numbers or their representation.
The word "solution" comes from the Latin word "solutio", which means "loosening" or "untying". It is derived from the verb "solvere", meaning "to loosen" or "to untie". In the context of problem-solving, a solution refers to the result or answer that resolves the given problem.
Therefore, the term "numerical solution" combines the concept of numbers with problem-solving, stating the idea of finding a solution to a problem using numerical methods or techniques.
