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In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
In mathematics, the method of characteristics is a technique for solving partial differential equations.Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation.
Method of lines - the example, which shows the origin of the name of method. The method of lines (MOL, NMOL, NUMOL [1] [2] [3]) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized.
In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms.They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture.
A partial differential equation is hyperbolic at a point provided that the Cauchy problem is uniquely solvable in a neighborhood of for any initial data given on a non-characteristic hypersurface passing through . [1]
The general solution to the first order partial differential equation is a solution which contains an arbitrary function. But, the solution to the first order partial differential equations with as many arbitrary constants as the number of independent variables is called the complete integral.
Whichever method we choose to solve this problem, we will need to solve a large linear system of equations. The reader may recall linear systems of equations from high school, they look like this: 2a + 5b = 12 (*) 6a − 3b = −3. This is a system of 2 equations in 2 unknowns (a and b). If we solve the BVP above in the manner suggested, we ...
The Adomian decomposition method (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations.The method was developed from the 1970s to the 1990s by George Adomian, chair of the Center for Applied Mathematics at the University of Georgia. [1]