Abstract
The nonstationary thermal state of a thermally sensitive multilayer plate is described by a nonlinear boundary-value problem with discontinuous coefficients. The method proposed for the construction of the solution of this boundary-value problem includes the transition to the Goodman integral variable, which enables us to regroup the nonlinearities and apply the integro-interpolation method for the construction of a semidiscrete analog of the model in the form of the Cauchy problem for a system of nonlinear ordinary differential equations. The obtained system of nonlinear ordinary differential equations for the Goodman variable is solved numerically with the help of multistep linear difference methods.
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