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Short answer; there isn't any.
Long/picky answer; numerical methods tend to look at, surprisingly, numerical methods on solving certain problems such as finding answers to equations (finding fixed points), calculating errors and really just doing calculations using these methods.
Numerical analysis on the other hand, does all of this but also looks deeper into why error occurs from these methods and looks into ways of adjusting these methods or developing better ones that reduce the errors given so as to obtain much more accurate approximations to the solution you are trying to find for a given problem.
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Definition of numerical analysis?
Numerical Analysis - an area of mathematics that uses various numerical methods to find numerical approximations to mathematical problems, while also analysing those methods to see if there is any way to reduce the numerical error involved in using them, thus resulting in more reliable numerical methods that give more accurate approximations than previously.
What is the difference between Applied Mathematics and Computational Sciences?
Applied mathematics is a very general term and thus makes this question rather difficult to answer, as it can apply to almost anything where advanced mathematics is used in the study topic. For example: probability, statistics, financial analysis, mechanics, physics, discrete mathematics, graph theory, engineering, numerical analysis, and even cryptology, can all be described as applied mathematics.The one that has the most in common with computer science however is, to my knowledge, numerical analysis. numerical analysis looks at problems in continuous mathematics that can't be solved by conventional analytical methods, and looks at developing algorithms to then solve these problems.Computer science looks at the theory behind information and computation/programming, and applies it to every area, using programmes and software to solve all problems, instead of just the ones looked at by numerical analysis.
What are the applications of numerical method?
Numerical methods are used to find solutions to problems when purely analytical methods fail.
What is the theory of finite differential method?
Finite Differential Methods (FDM) are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.
What is the difference between the graphical and numerical methods of finding the solution of an equation?
The graphical method is often approximate but can be applied to any function. If done on a computer, the region surrounding the solution can be enlarged to obtain more accurate estimates. A numerical method will give an exact result is an analytical solution is possible. If not, the solution will depend on the numerical method used and, sometimes, the starting "guesstimate".
