LM257 Boost Converter to 12V

I need a compact boost-converter design built around the LM257 that will take an input anywhere between 3 V and 5 V and reliably produce 12 V. The main objective is simply to raise the voltage—efficiency tweaks are welcome, but only if they keep the 12 V output rock-solid.

Please size and choose every supporting component, show the calculations that justify your values, and package everything so I can reproduce or tweak the design later. A quick simulation (LTspice, Proteus, or similar) or bench data that proves the circuit holds 12 V ±5 % across the full input range will close the loop.

Deliverables
• Annotated schematic (PDF + native CAD)
• Bill of materials with readily available parts
• Short design note covering formulas, expected efficiency, and a simple test plan

Once the documentation demonstrates a stable 12 V from any 3–5 V input, the job is complete.