Mathematical Proceedings of the Cambridge Philosophical Society · 1947 · 3.3K citations · 6 references
Natural SciencesMathematicsPhysicsDifferential EquationsHeat TransferThermodynamicsHeat ConductionHeat Transfer AnalysisHeat Transfer ModelingNumerical AlgorithmsNumerical Methods For Differential EquationsPartial Differential EquationsGeneral Heat Conduction EquationHeat Conduction EquationHeat EquationNonlinear Partial Differential EquationsNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsParabolic Partial Differential EquationsPartial Differential Equation Solvers
This paper is concerned with methods of evaluating numerical solutions of the non-linear partial differential equation where subject to the boundary conditions A, k, q are known constants. Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2).
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