Analog arithmetic circuit with electric resistor networks and numerical solution method of fourth-order partial differential equation by the use of the circuit

A method of solving a fourth-order partial differential equation of a function by the use of an analog arithmetic circuit comprising:

• a first resistor network comprising a plurality of first resistors connected to each other in a form of a lattice structure to have a plurality of first interconnected points arranged in a matrix form and a plurality of additional resistors having one ends connected to said first interconnected points, respectively, said first resistor network having a plurality of first peripheral terminals at outer ends of outermost ones of said first resistors, said first interconnected points classified into outermost ones and the remaining ones;
• a plurality of subtracting means having first input terminals connected to said remaining first interconnected points, respectively, second input terminals, and output terminals connected to the other ends of said additional resistors, respectively;
• a second resistor network comprising a plurality of second resistors connected to each other in a form of a lattice structure to have a plurality of second interconnected points arranged in a matrix form and corresponding to said remaining first interconnected points, respectively, said second resistor network having a plurality of second peripheral terminals at outer ends of outermost ones of said second resistors, said second peripheral terminals corresponding to said first peripheral terminals, respectively, said second interconnected points being connected to said second input terminals of said subtracting means, respectively;
• a plurality of calculating means connected to said second peripheral terminals, respectively;
• said method comprising the steps of:
• supplying external voltages of first predetermined voltage levels to said first terminals and said calculating means, respectively, first resultant voltages being present at said remaining first interconnected points;
• supplying boundary voltages of second predetermined voltage levels to said outermost first interconnected points and said calculating points, each of said calculating means calculating a total voltage of one of said external point voltages supplied to a corresponding one of said first peripheral terminals, two of said boundary voltages supplied to two adjacent to the corresponding one of said outermost first interconnected points, and one of said first resultant voltages on the adjacent one of said remaining ones of said first interconnected points adjacent to said corresponding one of said outermost first interconnected points, and subtracting four times of one of said boundary voltages supplied to said corresponding one of said outermost first interconnected points from said total voltage to produce a calculated voltage, said calculated voltage being supplied to the corresponding one of said second external terminals, whereby second resultant voltages are present at said second interconnected points, said subtracting means subtracting said second resultant voltages from said first resultant voltages to produce subtracted voltages, said subtracted voltages being supplied to said other ends of said additional resistors, so that said first resultant voltages provide solutions of said function of said fourth-order partial differential equation.