Divergence of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si9.svg" display="inline" id="d1e1285"> <mml:mi>θ</mml:mi> </mml:math> -Euler–Maruyama method for neutral stochastic differential equations with unbounded time-dependent delay and Markovian switching when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.svg" display="inline" id="d1e1290"> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo linebreak="goodbreak" linebreakstyle="after">∈</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:mrow> </mml:math>