Editing Partial differential equation (section)

===Superposition principle===
{{further| Superposition principle }}
The superposition principle applies to any linear system, including linear systems of PDEs. A common visualization of this concept is the interaction of two waves in phase being combined to result in a greater amplitude, for example {{math|1=sin ''x'' + sin ''x'' = 2 sin ''x''}}. The same principle can be observed in PDEs where the solutions may be real or complex and additive. If {{math|''u''<sub>1</sub>}} and {{math|''u''<sub>2</sub>}} are solutions of linear PDE in some function space {{mvar|R}}, then {{math|1=''u'' = ''c''<sub>1</sub>''u''<sub>1</sub> + ''c''<sub>2</sub>''u''<sub>2</sub>}} with any constants {{math|''c''<sub>1</sub>}} and {{math|''c''<sub>2</sub>}} are also a solution of that PDE in the same function space.