Partial Differential Equations

Scientific Notebook can solve a variety of linear partial differential equations of the first or second order; that is, equations of the form

A$\displaystyle {\frac{{\partial u}}{{\partial x}}}$ + B$\displaystyle {\frac{{\partial u}}{{\partial y}}}$ + Cu = E

or

A$\displaystyle {\frac{{\partial ^{2}u}}{{\partial x^{2}}}}$ + B$\displaystyle {\frac{{\partial ^{2}u}}{{\partial
x\partial y}}}$ + C$\displaystyle {\frac{{\partial ^{2}u}}{{\partial y^{2}}}}$ + E$\displaystyle {\frac{{\partial u}}{{%
\partial x}}}$ + F$\displaystyle {\frac{{\partial u}}{{\partial y}}}$ + Gu = H

where A, B, C, E, F, G, and H are constants or functions of x and y. These equations can also be written using the operator notation

ADxu + BDyu + Cu = E

or

ADxxu + BDxyu + CDyyu + EDxu + FDyu + Gu = H

Other traditional notation, such as uxy, may not be recognized.



Subsections