Sobolev spaces replace spaces of distributions when considering singularities in these equations.
Different solutions to equations of this type can be interrelated using an auto-BÃ¤cklund transformation. Some strategies for solving equations of this type only converge when the Courant number is less than one. Sobolev spaces replace spaces of distributions when considering singularities in these equations. One method for solving these equations seeks to find a parametric curve along which this type of equation reduces to a system of simpler equations. These equations can be solved on a discrete lattice using (*) finite element and finite difference methods, and they can be solved analytically by the method of characteristics. One hyperbolic equation of this type has a solution that varies sinusoidally in space and time; that is the wave equation. For 10 points, what equations can be simplified by separation of variables to produce multiple ordinary differential equations?
Different solutions to equations of this type can be interrelated using an auto-BÃ¤cklund transformation.
partial differential equations [or PDEs; prompt on differential equations; accept more specific answers like hyperbolic partial differential equations]