"Method is a particular way of doing something, sometimes also called an algorithm or procedure. (According to Petkovšek et al. (1996), "a method is a trick that has worked at least twice.")" [1]

"An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point. Specific algorithms sometimes also go by the name method, procedure, or technique.

The word "algorithm" is a distortion of al-Khwārizmī, a Persian mathematician who wrote an influential treatise about algebraic methods. The process of applying an algorithm to an input to obtain an output is called a computation" [2]

[1] http://mathworld.wolfram.com/Algorithm.html

[2] http://mathworld.wolfram.com/Method.html

Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, p. 117, 1996. http://www.cis.upenn.edu/~wilf/AeqB.html.

In mathematics and computer science, an algorithm is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning.

A procedure that has all of the characteristics of an algorithm except that it possible lacks finiteness may be called a computational method.

An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function.

Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input

https://en.wikipedia.org/wiki/Algorithm

http://stackoverflow.com/questions/879015/what-is-the-difference-between-an-algorithm-and-a-method

www.springer.com/cda/content/.../cda.../9783642214332-c2.pdf?...0...

Dear Colleagues,

Good Day,

A method (or message) in object-oriented programming (OOP) is a procedure associated with an object class. An object is made up of behavior and data. Data is represented as properties of the object and behavior as methods. Methods are also the interface an object presents to the outside world. For example a window object would have methods such as open and close. One of the most important capabilities that a method provides is method overriding. The same name (e.g., area) can be used for multiple different kinds of classes. This allows the sending objects to invoke behaviors and to delegate the implementation of those behaviors to the receiving object. For example an object can send an area message to another object and the appropriate formula will be invoked whether the receiving object is a rectangle,circle, triangle, etc.

Methods also provide the interface that other classes use to access and modify the data properties of an object. This is known as encapsulation. Encapsulation and overriding are the two primary distinguishing features between methods and procedure calls.

In mathematics and computer science, an algorithm ( i/ˈælɡərɪðəm/ al-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning.

An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output"and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.

The concept of algorithm has existed for centuries, however a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included theGödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.

Please, see the links for details

https://en.wikipedia.org/wiki/Method_(computer_programming)

https://en.wikipedia.org/wiki/Algorithm

Dear @Subhash C. Kundu,

Thank you very much for opinion. 

Best regards, Shafagat

Dear @Hazim Hashim Tahir,

Thank you very much for interesting answer.

Best regards, Shafagat

Thank you Hazim for the interesting answer

"Method is a particular way of doing something, sometimes also called an algorithm or procedure. (According to Petkovšek et al. (1996), "a method is a trick that has worked at least twice.")" [1]

"An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point. Specific algorithms sometimes also go by the name method, procedure, or technique.

The word "algorithm" is a distortion of al-Khwārizmī, a Persian mathematician who wrote an influential treatise about algebraic methods. The process of applying an algorithm to an input to obtain an output is called a computation" [2]

[1] http://mathworld.wolfram.com/Algorithm.html

[2] http://mathworld.wolfram.com/Method.html

Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, p. 117, 1996. http://www.cis.upenn.edu/~wilf/AeqB.html.

In my opinion, an algorithm is a series of steps (a process) for performing a calculation. On the other hand, methodology is more general form of any solution. it provided a way how to solve any problem.

In another point of view:

"method (n.)

early 15c., "regular, systematic treatment of disease," from Latin methodus "way of teaching or going," from Greek methodos "scientific inquiry, method of inquiry, investigation," originally "pursuit, a following after," from meta- "after" (see meta-) + hodos "a traveling, way" (see cede). Meaning "way of doing anything" is from 1580s; that of "orderliness, regularity" is from 1610s. In reference to a theory of acting associated with Russian director Konstantin Stanislavsky, it is attested from 1923.

algorithm (n.) 

1690s, from French algorithme, refashioned (under mistaken connection with Greek arithmos "number") from Old French algorisme "the Arabic numeral system" (13c.), from Medieval Latin algorismus, a mangled transliteration of Arabic al-Khwarizmi "native of Khwarazm," surname of the mathematician whose works introduced sophisticated mathematics to the West (see algebra). The earlier form in Middle English was algorism (early 13c.), from Old French."

"Online Etymology Dictionary"

http://www.etymonline.com/index.php?search=algorithm+method&searchmode=or

Dear @Behrouz Ahmadi-Nedushan,

Thank you very much for opinion.

Best regards, Shafagat

Dear @Barbara Sawicka,

Thank you very much for opinion.

Regards, Shafagat

Dear  @Seyed Mehdi Mohammadizadeh,

Thank you very much for interesting answer.

Regards, Shafagat

Your question is of specification vs. general type. Algorithm usually refers to the specific steps used to end up with the result after mathematical processing, but method is a general way of doing something (especially in a planned or established way).Algorithm is a precise set of rules or an abstract concept specifying how to solve a given problem. 

Dear Mahmoud Omid,

Thank you very much for opinion. The difference between them is not felt.

Regards, Shafagat

According to "Online Oxford Dictionaries" (http://www.oxforddictionaries.com), the words in question are defined as follows:

algorithm:

A process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer:

'a basic algorithm for division'

method:

A particular procedure for accomplishing or approaching something, especially a systematic or established one:

'a method for software maintenance'

'labour-intensive production methods'

Thus, "algorithm" is used in mathematical situations, while "method" can be used in more general situations.

Actually an algorithm is a method, technique or recipe for doing something in computer. Algorithms is a pseudo code which tells you how to accomplish a task by performing a number of steps. The essential feature of an algorithm is that it is made up of a finite set of operations that are unambiguous and simple to follow. 

So maybe this example may help you: To bake a cake we use a method or a special recipe: These are the steps: preheat the oven; mix flour, sugar, and eggs thoroughly; pour into a baking pan; and so forth. However, algorithm is a technical term with a more specific meaning than “recipe”. it specifies a series of steps that perform a particular computation or task. It must meet the following criterion: have inputs and outputs, be unambiguous, guaranteed to terminate in finite steps, and produces the correct result.

to give you an example and explain.

Problem: multiply two large matrices. 

method 1: use a stand alone computer

method 2: use distributed system 

Algorithm: standard algorithm which works on stand alone system to find matrix multiplication with complexity of big-oh(n^3). or use strassen's matrix multiplication algorithm with complexity big-oh(n^2.71). Strassen's algorithm can also be implemented using method 2. 

Hi,

I agree with you on your definition:

Algorithm - a set of instructions that describe the procedures artist to achieve the result of solving the problem in a finite number of steps, for any set of input data.

Method  - systematic set of steps, actions, which are aimed at solving a particular problem or to achieve a certain goal.

I may also add that the method may include several algorithms which are established to achieve the goal.

Dear Shafagat Mahmudova,

In the before made responses, you have got excellent answers... is harder to say something new... I have made also an algorithm to determine tide effect onto Mercury, Venus and Moon... verified with Earth tides..... From this my simle opinion is>

The every algorithms are methods... But  not all methods are algorithm... Example Mohs scale of mineral hardness is a method... In Earth Science, Planetology, Cosmology... are using lot of methods which at same time are not algorithms... In math, computer sciences (software creations), physics and rear case in Earth sciences, planetology, Cosmology we are create algorithms that are methods...    

In the context of computability theory there was defined what an algorithm is. A method wants to achieve a certain goal, possibly incolving several algorithms.

a method is a more general concept than algorithm and can be more or less anything, e.g. writing data to a file. Just about anything that should happen due to an event or to some logical expression. Also, the meaning of the words "method" and "algorithm" can vary depending on in what context they are used. They might be used to describe the same thing.

As I understand, method is more general, since it has many guides and ruless at its definition.

On the other side, algorithm is a very specific set of commands that have to be executed in order to apply a method.

A method is the way a particular problem can be solved, while an algorithm is the orderly steps following them the solution can be computed. Method can be abstract form while algorithm is systematic steps. Algorithm can be implemented on a computer.

Interesting and tricky question. I do agree with @R.C. Mittal. 

Algorithm would involve step by step procedures while a method may not.

Very nice and brief answer from dear @ Pelumi Oguntunde:

Algorithm would involve step by step procedures while a method may not.

I fully endorse it.

Already many good explanations have been given . So I will keep it short. Ithink method can be treated as a superset of algorithm. If given proper input, the algorithm will always work but the method may not. For example, if given a system of equations, Gauss elimination(an algorithm) can be used to solve it. But consider a finite difference method which reduces a differential equation to a system of equations which can be solved by Gauss elimination. Clearly, in this case, the algorithm is a subset of the method. All finite difference method are not stable i.e. they does not fulfill our requirement.

In chemistry, we consider a method as a way, technique, or process for doing something. Whereas an algorithm is a step-by-step procedure followed for solving a problem or accomplishing some end. To illustrate: Assume that there is a solution which has hydrogen ion concentration of 1.0 × 10 -3 molar , will this solution be acidic or basic ? We can find out the answer by different methods (difficult to program in computer) but the algorithm procedure will be restrictive or specific (easy to program in computer) & will be: pH = -log [H+] = -log[1.0 × 10-3] =3. According to the pH scale,a solution is acidic if its pH is < 7

Dear Dr. Dear Shafagat Mahmudova,

There is no technical difference between the term method and algorithm.

Method is an established, habitual, logical, or prescribed practice or systematic process of achieving certain ends with accuracy and efficiency. To achieve this it usually desirable to split the process into sub-processes (functions) and organize the tasks  in an ordered sequence of fixed steps (algorithm).

Algorithm is the resolution scheme of a problem, it describes the steps that a computer program should fulfills to meet with the correct solution, prediction, organization or estimation. The resolution scheme is based on scientific approaches, theorems, equations, or methods needed for processing the input data. In one algorithm several approaches could be used.

Algorithm is a set of steps to follow intended to solve a specific problem. Mathematical equations are algorithms; so are computer programs. The service people who fix copying machines and other office or household equipment are trained to use a series of tests in a particular sequence that quickly identify the problem.

http://www.indiana.edu/~p1013447/dictionary/alg_heur.htm

Method is used to determine a feasible solution that may or may not be optimal

http://www.cs.umsl.edu/~sanjiv/classes/cs5130/lectures/gm.pdf

Dear @ Krishnan wrote:

"Method is used to determine a feasible solution that may or may not be optimal"!!

 This is not a general definition of method at all.

I was surprised and I referred to his attached document:

http://www.cs.umsl.edu/~sanjiv/classes/cs5130/lectures/gm.pdf

The document discusses greedy methods which are used in optimization problems and does not provide a general definition of method.

Let's see the definitions of method in dictionaries:

Method: careful or organized plan that controls the way something is done

http://www.merriam-webster.com/dictionary/method

Method: A particular procedure for accomplishing or approaching something, especially a systematic or established one:

http://www.oxforddictionaries.com/definition/english/method

Method:  way of doing something, especially a planned or established way

http://www.macmillandictionary.com/dictionary/british/method

It is difficult to define them separately.

a METHOD is the basic strategy to organize the collection of operands and operators such that, that an ALGORITHM working on it for a specific purpose, can have a certain quality (more efficient, faster, more flexible, etc.).

A  method is a more general concept than algorithm. In engineering, we can use analytical . numerical or experimental methods to model a process/problem. Each method, we may use different algorithms (and possibly more than one algorithm) to solve the problem. Moreover, Algorithms terminate in a finite number of steps.

The following taken from attached link is very informative and provides a clear definition of an algorithm in the context of CS:

"The computer scientist Niklaus Wirth stated that:

Programs = Algorithms + Data

The algorithm is part of the blueprint or plan for the computer program, an algorithm is:

"An effective procedure for solving a problem in a finite number of steps."

It is effective, which means that an answer is found and it finishes, that is it has a finite number of steps. A well-designed algorithm will always provide an answer, it may not be the answer you want but there will be an answer. It may be that the answer is that there is no answer. A well-designed algorithm is also guaranteed to terminate.

Here is an example of an algorithm for making a pot of tea:

• If the kettle does not contain water then fill the kettle
• Plug the kettle into the power point and switch it on.
• If the teapot is not empty then empty the teapot.
• Place tea leaves in the teapot.
• If the water in the kettle is not boiling then go to step 5
• Switch the kettle off.
• Pour water from the kettle into the teapot.

You can see that the algorithm has a number of steps, that some steps (steps 1, 3 and 5) involve decision-making and one step (step 5) involves repetition, in this case the process of waiting for the kettle to boil.

Algorithms show these three features:

• Sequence (also known as Process)
• Decision (also known as Selection)
• Repetition (also known as Iteration or Looping)"

http://users.evtek.fi/~jaanah/IntroC/DBeech/3gl_algorithm1.htm

Method is logic-based (of Wisdom and Science). Algorithm is logic-developed (of Intelligence and Engineering).

Method is procedure, technique, system but algorithm may be part of the method.

Algorithm is systematic combination of data and control flow with different directions. While method  is particular way of procedure with nearly same sequence.  Method is combination of actions. Action is made of all different states. All the combination of states is the one event . Then combination of all events with control becomes behavior. This behavior can be represented by algorithm.

This algorithm is called a finite group of logic operations organized and orderly way which allows to solve a particular problem. This is a series of instructions or rules established by means of a succession of steps, allowing to reach an outcome or solution.

While the method refers to the manner or way of doing something in a systematic, organized and / or structured. It refers to a technique or set of tasks to perform a task. The word method may refer to various concepts. For example, methods of scientific classification, the scientific method, the statistical method etc.

Dear Colleagues,

Good Day,

Algorithm is just like a formula to solve any particular problem step by step,with no ambiguity to any step, and must have some ending point.

methodology is more general form of any solution. it provided a way how to solve any problem but in algorithm the way is more precisely formulated towards solution.

In my opinion, method is subset of algorithm. A method is normally used to solve a particular type of problems whereas, an algorithm used to solve the complete problem from start to end through various steps.

How does "scheme" differs from "algorithm"?

Thanks and regards,

Senthil Kumar

https://www.quora.com/What-is-the-difference-between-a-method-and-an-algorithm