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Separation of variables

In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.

Art, Partial differential equations & Ordinary differential equations (ODE)

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Overview

Ordinary differential equations (ODE)

Partial differential equations

Matrices

Software

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Separation of variables

Nodes42
Edges41
Triples48
Avg. degree1.95
Density0.047619
Components1

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Separation of variables

Top relations

related to External links · 19
Separation of variables → Differential Equation, EMS Press, Encyclopedia, EqWorld, Eric, Fourier, Functional Separation, Generalized, John Renze, Mathematical EquationsExamples, Mathematics, MathWorld, Methods, PDEs, Separation, Short Justification, The World, Variables, Weisstein
related to Partial differential equations · 10
Separation of variables → Below, Consider, For, Helmholtz, In, Laplace, PDEs, Schrödinger, Separation, The
related to Curvilinear coordinates · 4
Separation of variables → Cartesian, For, In, See
related to Matrices · 4
Separation of variables → As, Kronecker, Laplacian, The
related to Example: mixed derivatives · 3
Separation of variables → Consider, For, Proceeding
is a · 2
Separation of variables → Kronecker sum.As an example we consider the 2D discrete Laplacian on a regular grid, result of the spectral theorem
related to Alternative notation · 2
Separation of variables → Integrating, Those
related to Example · 2
Separation of variables → Population, Separation
related to Software · 2
Separation of variables → Some, Xcas

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Important terminology

displaystyle equation differential variables separation equations boundary separable partial condition method two side form dx may respect left get one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Separation of variablesis aresult of the spectral theorem0.90text
Separation of variablesis aKronecker sum.As an example we consider the 2D discrete Laplacian on a regular grid0.90text
Separation of variablesrelated to Alternative notationThose0.60section
Separation of variablesrelated to Alternative notationIntegrating0.60section
Separation of variablesrelated to Curvilinear coordinatesIn0.60section
Separation of variablesrelated to Curvilinear coordinatesCartesian0.60section
Separation of variablesrelated to Curvilinear coordinatesFor0.60section
Separation of variablesrelated to Curvilinear coordinatesSee0.60section
Separation of variablesrelated to ExamplePopulation0.60section
Separation of variablesrelated to ExampleSeparation0.60section
Separation of variablesrelated to Example: mixed derivativesFor0.60section
Separation of variablesrelated to Example: mixed derivativesConsider0.60section

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