The present paper proposes an approximate method to simplify a family of general equations linked to linear (1+1) parabolic equations. That is, we consider some complicated equations as perturbations to parabolic equations, thereby decomposing a challenging problem into a number of relatively easier ones. We introduce a mapping which transforms the equation to a version of the heat equation. It is then possible to find approximate solutions of these equations. The approach is illustrated by several examples including the KPP Fisher equation, a general Huxley equation and a nonlinear Black-Scholes equation.
Jamal, S. (2026). Approximating families of nonlinear equations by linear parabolic equations. (e742142). Mathematics and Computational Sciences, (), e742142 https://doi.org/10.30511/mcs.2026.2075410.1552
MLA
Jamal, S. "Approximating families of nonlinear equations by linear parabolic equations" .e742142 , Mathematics and Computational Sciences, , 2026, e742142. doi: 10.30511/mcs.2026.2075410.1552
HARVARD
Jamal S. (2026). 'Approximating families of nonlinear equations by linear parabolic equations', Mathematics and Computational Sciences, (), e742142. doi: 10.30511/mcs.2026.2075410.1552
CHICAGO
S. Jamal, "Approximating families of nonlinear equations by linear parabolic equations," Mathematics and Computational Sciences, (2026): e742142, doi: 10.30511/mcs.2026.2075410.1552
VANCOUVER
Jamal S. Approximating families of nonlinear equations by linear parabolic equations. MCS. 2026;():e742142. doi: 10.30511/mcs.2026.2075410.1552
