Linearity in solvers refers to problems where the relationship between input and output can be expressed as a linear equation, making them computationally efficient and predictable. Nonlinearity introduces complex interactions between variables, often requiring iterative, approximate methods to find solutions, which can be computationally expensive and less predictable.
Analytical solutions provide an exact answer to a mathematical problem expressed in terms of well-known functions, while numerical solutions use computational methods to approximate the answer, often useful when analytical approaches are impractical. The choice between them depends on the nature of the problem, available computational resources, and the required precision.