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A cellular neural network for solving a class of partial differential equations is presented. Each neural cell consists of a novel floating variable linear resistor, an amplifier, and a passive capacitor. The output of each cell is integrated with a microelectromechanical (MEMS) heater device that will be used for a thermal interface. The CMOS VLSI implementation of a nine cell network was designed and simulated. The results of this network are compared to the numerical solution of the partial differential equations.