Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
Well drainageWell drainage means drainage of agricultural lands by wells. Agricultural land is drained by pumped wells (vertical drainage) to improve the soils by controlling water table levels and soil salinity. Subsurface (groundwater) drainage for water table and soil salinity in agricultural land can be done by horizontal and vertical drainage systems. Horizontal drainage systems are drainage systems using open ditches (trenches) or buried pipe drains. Vertical drainage systems are drainage systems using pumped wells, either open dug wells or tube wells.
Agricultural hydrologyAgricultural hydrology is the study of water balance components intervening in agricultural water management, especially in irrigation and drainage. The water balance components can be grouped into components corresponding to zones in a vertical cross-section in the soil forming reservoirs with inflow, outflow and storage of water: the surface reservoir (S) the root zone or unsaturated (vadose zone) (R) with mainly vertical flows the aquifer (Q) with mainly horizontal flows a transition zone (T) in which vertical and horizontal flows are converted The general water balance reads: inflow = outflow + change of storage and it is applicable to each of the reservoirs or a combination thereof.
SahysModSahysMod is a computer program for the prediction of the salinity of soil moisture, groundwater and drainage water, the depth of the watertable, and the drain discharge in irrigated agricultural lands, using different hydrogeologic and aquifer conditions, varying water management options, including the use of ground water for irrigation, and several crop rotation schedules, whereby the spatial variations are accounted for through a network of polygons.
Finite-state machineA finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a transition. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition.
Nondeterministic finite automatonIn automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its source state and input symbol, and reading an input symbol is required for each state transition. A nondeterministic finite automaton (NFA), or nondeterministic finite-state machine, does not need to obey these restrictions. In particular, every DFA is also an NFA. Sometimes the term NFA is used in a narrower sense, referring to an NFA that is not a DFA, but not in this article.
Deterministic finite automatonIn the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running through a state sequence uniquely determined by the string. Deterministic refers to the uniqueness of the computation run.
Boussinesq approximation (water waves)In fluid dynamics, the Boussinesq approximation for water waves is an approximation valid for weakly non-linear and fairly long waves. The approximation is named after Joseph Boussinesq, who first derived them in response to the observation by John Scott Russell of the wave of translation (also known as solitary wave or soliton). The 1872 paper of Boussinesq introduces the equations now known as the Boussinesq equations. The Boussinesq approximation for water waves takes into account the vertical structure of the horizontal and vertical flow velocity.
Unambiguous finite automatonIn automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. Each deterministic finite automaton (DFA) is an UFA, but not vice versa. DFA, UFA, and NFA recognize exactly the same class of formal languages. On the one hand, an NFA can be exponentially smaller than an equivalent DFA. On the other hand, some problems are easily solved on DFAs and not on UFAs.
