More on standing waves in a dipole antenna
Radio engineers meet often cases where a reflection happens at the end of a transmission line, but the signal still doesn't reflect towards the source, the structure is a matching stub which is inserted to direct all fed signal to the load which alone would be mismatched with the feeding line.
The antenna which isn't big when compared to the wavelength must be seen as one item, there's no parts that coming waves could see separately. The idea &quot;wave reaches at first the feeding point, propagates to the ends of the dipole rods and reflects back towards the feeding point &quot; is a total misconception. How? Dipole rods are no more 2 parallel wires which guide the wave to propagate along a transmission line, the field around the rods must be handled as one unit and the wave equations must be solved simultaneously around the whole rods to get any idea what happens.
The known solution is that the wave spreads to the space and virtually nothing returns back to the feeding line if the line is matched to the dipole and the dipole is in tune at the used frequency. That result cannot be found otherwise than by solving as one piece the behaviour of the wave in the whole antenna and the space around it.
Many radio antenna books show how the radiation field of a dipole is derived by assuming a standing wave like sinusoidal current distribution along the rods. That's ok engineering approximation for many practical purposes, but the exact current distribution along the dipole rods is a little different and it cannot be derived properly without solving the wave equations in the space around the rods.
The fields around the dipole can be divided to 2 parts:

radiating wave
oscillating near field, which can have reactive power in VA:s much bigger than the power of the radiating wave is in watts.

That big difference gives some justification to the idea there's a standing wave in the antenna. But the standing wave like behaviour is caused by the fact that virtually nothing returns to the feeding line, its not that there's a standing wave but some miracle (=explanation you are waiting for) stops the reflection to return to the feeding line.
ADD: The matching stub I mentioned in the beginning can be engineered with circuit theory and by following the total admittance of the loaded line with Smith's chart. One searches with the chart where the total admittance of the loaded line is 1/Zc + Yj where the real part 1/Zc is just the inverse of the line impedance and the imaginary part Y is what it happens to be. Then one inserts to the found place in parallel with the line the shorted or open ended stub which has total admittance -Yj. That makes the stub+the rest of the line+the load matched - no reflection to the source end, no matter there's standing wave in the stub and in the section between the stub and the load.
Actually the stub makes the backwards wave towards the source impossible. The engineering calculation happens in the world of voltages, currents, impedances and reflection factors, it doesn't a all care the actual E and H fields in the space around the wires.The working of the construction definitely happens in those fields, but fortunately there's quite good correspondence between the vector field effects and the circuit theory version.
We do not have proper circuit theory distributed element model for dipole rods. I guess you wanted something like inductor, capacitor and loss resistor ladder (=like the TEM transmission line element) which has a loss resistor in series with the inductor. In this case the capacitors decrease towards to rod ends and the resistors present the losses caused by the radiation. Assuming that model exists you hoped there's perfect matching achieved in the feeding point just like in the mismatched transmission line is tuned with the stub.
Unfortunately such model isn't well known - at least I haven't seen it. And scientifically it would be nonsense as long as nobody has proved the properly solved fields obey that model. In TEM transmission line theory mathematicians have found that Heaviside's ad-hoc LRC ladder element approach fits with the properly solved E and H fields.