Volterra integral equations
E645176
Volterra integral equations are a class of integral equations, often used in physics and biology, where the integration limits involve a variable upper bound, modeling systems with memory or hereditary effects.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Volterra integral equation | 0 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf | integral equation ⓘ |
| appearsIn |
hereditary population models
ⓘ
mathematical biology ⓘ |
| canBeDiscretizedBy |
Galerkin methods
NERFINISHED
ⓘ
collocation methods ⓘ finite difference methods ⓘ |
| canBeTransformedTo | differential equation ⓘ |
| characterizedBy | integration over past history ⓘ |
| contrastedWith | Fredholm integral equation NERFINISHED ⓘ |
| hasApplication |
epidemiological models
ⓘ
hereditary mechanics ⓘ neutron transport ⓘ population growth with memory ⓘ viscoelasticity ⓘ |
| hasFirstKindForm | f(t) = ∫_a^t K(t,s) y(s) ds ⓘ |
| hasHistoricalDevelopmentPeriod | early 20th century ⓘ |
| hasIndependentVariable | time ⓘ |
| hasIntegrationLimitType | variable upper limit ⓘ |
| hasKernel | Volterra kernel NERFINISHED ⓘ |
| hasMathematicalForm | y(t) = f(t) + ∫_a^t K(t,s) y(s) ds ⓘ |
| hasProperty |
causal
ⓘ
initial-value character ⓘ triangular integration domain ⓘ |
| hasSecondKindForm | y(t) = f(t) + ∫_a^t K(t,s) y(s) ds ⓘ |
| hasSolutionSpace | function space ⓘ |
| hasType |
Volterra equation of the first kind
NERFINISHED
ⓘ
Volterra equation of the second kind NERFINISHED ⓘ linear Volterra integral equation ⓘ nonlinear Volterra integral equation ⓘ |
| hasVolterraOperator | Volterra integral operator NERFINISHED ⓘ |
| kernelDependsOn | time variables t and s ⓘ |
| models |
hereditary effects
ⓘ
systems with memory ⓘ |
| namedAfter | Vito Volterra NERFINISHED ⓘ |
| relatedTo |
Volterra series
NERFINISHED
ⓘ
convolution integral ⓘ |
| requiresCondition | kernel regularity for existence and uniqueness ⓘ |
| solvedBy |
Laplace transform
NERFINISHED
ⓘ
Neumann series NERFINISHED ⓘ quadrature methods ⓘ resolvent kernel method ⓘ successive approximations ⓘ |
| studiedIn |
functional analysis
ⓘ
integral equation theory ⓘ |
| usedIn |
biology
ⓘ
control theory ⓘ engineering ⓘ physics ⓘ population dynamics ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.