A **solver** is a generic term indicating a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculate their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type.

Types of problems with existing dedicated solvers include:

- Linear and non-linear equations. In the case of a single equation, the "solver" is more appropriately called a root-finding algorithm.
- Systems of linear equations.
- Nonlinear systems.
- Systems of polynomial equations, which are a special case of non linear systems, better solved by specific solvers.
- Linear and non-linear optimisation problems
- Systems of ordinary differential equations
- Systems of differential algebraic equations
- Logic/satisfiability problems
- Constraint satisfaction problems
- Shortest path problems
- Minimum spanning tree problems
- Search algorithms

The General Problem Solver (*GPS*) is a particular computer program created in 1957 by Herbert Simon, J.C. Shaw, and Allen Newell intended to work as a universal problem solver, that theoretically can be used to solve every possible problem that can be formalized in a symbolic system, given the right input configuration. It was the first computer program which separated its knowledge of problems (in the form of domain rules) from its strategy of how to solve problems (as a general search engine).

General solvers typically use an architecture similar to the GPS to decouple a problem's definition from the strategy used to solve it. While the strategy utilized by GPS was a general algorithm with the only goal of completeness, modern solvers tend to use a more specialized approach tailored to the specific problem class which the solver aims for. The advantage in this decoupling is that the solver doesn't depend on the details of any particular problem instance.

For problems of a particular class (e.g., systems of non-linear equations) there are usually a wide range of different algorithms available; sometimes a solver implements multiple algorithms, but sometimes just one.

### Other articles related to "solver, solvers":

**Solver**

... TK

**Solver**(originally TK!

**Solver**) is a mathematical modeling and problem solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc ...

... argv) { LIS_MATRIX_A_LIS_VECTOR b,x LIS_SOLVER

**solver**LIS_INT iter double times lis_initialize( argc, argv) lis_matrix_create(LIS_COMM_WORLD, A) lis_vector_create(LIS_COMM_WORLD, b) lis_vector_create(LIS_C ...

... hybrid meshes in many formats Numerical Methods Cell Center finite volume

**solver**Residual distribution

**solver**High order finite element

**solver**Spectral Finite Volume

**solver**Spectral Finite Difference ...

**Solver**

... The Concorde TSP

**Solver**is a program for solving the traveling salesman problem ... state of the art implementation” and state that it is “one of the best exact TSP

**solvers**currently available.” Mulder Wunsch (2003) add that Concorde “is ...

**Solver**Approaches

... on the bits) and passing this formula to a Boolean SAT

**solver**... formula we can use existing Boolean SAT

**solvers**"as-is" and leverage their performance and capacity improvements over time ... theories means that the Boolean SAT

**solver**has to work a lot harder than necessary to discover "obvious" facts (such as for integer addition.) This observation led to the development of a number of SMT

**solvers**that ...