implicit methods

Implicit methods are numerical techniques used to solve mathematical problems, especially differential equations. Unlike explicit methods, which calculate the state of a system based solely on current or past information, implicit methods involve solving an equation that includes the unknown future state. This approach typically requires more computation per step but offers greater stability, allowing larger steps and better handling of stiff problems. Essentially, implicit methods look ahead and incorporate future information directly into the calculation, making them reliable for complex or sensitive systems where explicit methods might fail or become unstable.