## Inconvenience of numerical solution

##### Inconveniences of Numerical Solutions

Numerical solution seems to be not the appropriate one even if it is doable and the only one left so far because the loss of the potential of features and attributes with which the missing exact solution formula describes the case physical dependence and the afterward mathematical model, a typical vague picture, things get more vaguely if the equation is a function of itself, self dependent, i.e. function of the dependent variable the equation would have meant to be solved for also there some challenges like where there is a differentiation in a denumerator in the differential equation; this vaguely situation decreases the power of the tools used in design dramatically, all this because there is no a formula describe such.

##### Numerical Solutions

**Definition**: Numerical solutions involve approximating the solution of an equation using computational methods. These approaches iteratively refine estimates until they reach a desired level of accuracy.##### Single or Multiple Variables Function Iteration

Adaptive iteration techniques ensure that solutions converge more reliably, making the process of finding roots or optimizing functions more efficient.

##### Convergence vs. Diverse Iteration Solver

New solvers can distinguish between convergent and divergent iterations, adapting their approach accordingly to ensure solutions are found where possible.