SU1501054A1 - Digital integrator for solving terminal problems - Google Patents

Abstract

The invention relates to digital computing and is intended for the construction of digital integrating machines. The purpose of the invention is to improve the accuracy of calculations. The integrator contains the adder 1 of the integrand function, the register 3 of the integrand function, the first multiplication unit 4, the adder 5 of the integral residue, the switch 6, the integral register 8, two adders 9, 10 of the variation interval of the first and second coordinates, the third and fourth multiplication blocks 12, 13, two adders 16, 17 unquantized variations of the integral in the first and second coordinates, two registers 18, 19 unquantized variations of the integral in the first and second coordinates, two elements AND 20, 21, inputs and outputs 2, 7, 11, 14, 15, 22-25. The goal is achieved by using an unquantized value of variation. 1 il.

Description

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The invention relates to digital computing and can be used in the development of digital integration machines for solving boundary and variational problems.

The purpose of the invention is to improve the accuracy of calculations.

The drawing shows an integrator schema.

HHTerpa i op contains the adder 1 of the integrand function, the input bus 2 increases the integrand function, the register 3 of the integrand function 15 integrates the following, the first block 4 multiplies in a summed manner.

In adder 1, the increment of the integrand function vt is added with its value., Arriving 20 from register 3, and its new value Cfp; is written in the same register. In addition, the tpp value; the integral remainder 5, the switch 6, the output increment bus 7 of the integral, the integral remainder register 8, two adders 9 and 10 integral residuals along the first and second coordinates, respectively, the input 1shn 11 increments of the integration function, the second 12 and the third 13 multiplication blocks, input tires 14 and 15 variations of the integrand with respect to the first and second coordinates, respectively; CTBeHHOj, two adders 16 and 17 unquantized variations of the integral with respect to

It goes to multiplication unit 4, where it is smart; It makes an increment to the integration function vt. Together with this, in blocks 12 and 13 multiplied by the increment V t, the variations of the integrating function XCC are multiplied) - ;, VygCfp;

on the first and second coordinates vt x

)

previous integration step;

o M, H (increment of the variation of the integral (difference of the second order);

- the remainder from quantizing the increments of the Riemann integral over time. Variables and increments marked with a dash above are quantized values of the corresponding values.

Integration at (1 + 1) -th step

In adder 1, the increment of the integrand function vt is added with its value coming from register 3 and its new value Cfp; is written in the same register. In addition, the tpp value; enters multiplication unit 4, where it is smart; The key is to increment the integration function vt. Together with this, in blocks 12 and 13 multiplied by the increment V t, the variations of the integrating function XCC are multiplied) - ;, VygCfp;

on the first and second coordinates respectively

the first and second coordinates are correspondingly ZO. Product Vtcf ,,

Actually, two registers 18 and 19 are unquantized variations of the integral over the first and second coordinates, respectively, two elements AND 20 and 21, output buses 22 and 23, variations of the integral pj of the first and second coordinates, respectively, control input 24 and clock input 25.

This integrator allows one to find the increments of the Riemann integral Vt | | j appeared when integrating the first-order differential equation and simultaneously two variations of it, with respect to disturbing the initial conditions XD and y, respectively, which ensures a higher speed of solving boundary problems in comparison with the digital integrator of functions of one variable.

In the integrator, the output value of the variation of the integral, for example, along the x coordinate is formed as a sum

35

 tfpjVt from the output of block 4 multiplies to the adder 5. The product, VXoq pj.Vt. and yo4 p -V t from the outputs of blocks 12 and 13 multiplications are fed to adders 16 and 17, where they fold with variations V XQ cf; coming from registers 18 and 19 with

responsibly. The resulting unquanto-4Q bath variations,, V, c; , from the outputs of the adders 16 and 17, entries are written to registers 18 and 19 and fed to adders 9 and 10, respectively. In adder 5, the unquantized increment of the integral VtCf ;, is combined with the remainder), coming from register 8. Formed suma v t Cf ;,. + 0 () goes further to the switch, where the quantized increment of the integral Vt + is allocated from it, and the new remainder is written to register 8. The remainder OCvtCj;) also goes to, adders 9 and 10, where it is added

50

VXjjU) VX (j C); -t-Vt -Xg q) ;, +0 (Vtqi ;;,. ,, combined variations of the integral

55

o H; -ti) according to the first second coordinates of the Formed sums V Xd L | ;,

where 1 is the step number of the integrator; VX (, qi, is the unquantized value of the variation of the integral on

five

 tfpjVt from the output of block 4 multiplies to the adder 5. The product, VXoq pj.Vt. and yo4 p -V t from the outputs of multiplication blocks 12 and 13 are fed to adders 16 and 17, where they add up to variations of V XQ cf; coming from registers 18 and 19 with

responsibly. The resulting unquantified Q variations of,, Vy, cf; The outputs of the adders 16 and 17 are recorded in registers 18 and 19 and fed to adders 9 and 10, respectively. In adder 5, the unquantized increment of the integral VtCf ;, is added to the remainder) coming from register 8. The sum v v Cf ;, is formed. + 0 () goes further to the switch where the quantized increment of the integral Vt + is removed from it, and a new remainder,) written to register 8. The remainder OCvtCj;) also goes to, adders 9 and 10, where it is added to

integral variations

o H; -ti) on the first and second coordinates, respectively. From the formed sums V Хд L | ;, +

+ OCvtlf;) and PP e;, + 0 (VtCf;) with po 515

by the power of the elements 20 and 21, quantized variations of the integral are obtained.

 och; +. (° first and second coordinates, respectively.

Claims (1)

Invention Formula Digital integrator for solving boundary value problems, containing the integrand function register, integrator function adder, three multiplication units, integral remainder adder, integral remainder register, switchboard and two AND elements, the input of the integrator integrand increment input to the input of the first adder of the integrand function, output which is connected to the input of the first multiplier of the first multiplication unit and the information input of the register of the integrand function, the output of which is connected to the input of the second The addendum addendum of the integrand function, the output of the first multiplication unit is connected to the input of the first adder of the remainder of the integral, the output of which is connected to the information input of the switch, the first output of which is connected to the output of the integral increment of the integrator, and the second output of the switch is connected to the information input of the integral remainder register, output which is connected to the input of the second term of the adder of the integral residue, the input of the increment of the integration function is connected to the inputs of the second factor ervogo, second and third multipliers, variations inputs integrand by the first coordinate and a second integrator connected to the first inputs of the second and third multipliers multiplying units, respectively, the outputs of the first and secondary jporo elements and connected to the outputs of the first integral variations and 10546 the second co-ordinator of the integrator, respectively, the integrator's control input is connected to the control input of the switch and the first inputs of the first and second elements AND, the clock input of the integrator is connected to the synchronization inputs of the register of the integrand function, the register Q residual integral and first, second, and third multiplication blocks, characterized in that, in order to improve the accuracy of calculations, two cyNMaTopa residual variations of the integral along the first and second coordinates were introduced into the cy, two adders of the unquantized variable of the first and second coordinates and two registers of unquantized variations of the integral over 20 of the first and second coordinates, with the outputs of the second and third multiplication blocks connected to the inputs of the first terms of adders of unquantized variations of the integral over the first 25 and the second coordinate, respectively, the outputs of which are connected to the inputs of the first components of the adders of the residuals of the integral variations in the first and second coordinates and information 3Q inputs of registers of unquantized variations of the integral with respect to the first and second coordinates, respectively, whose outputs are connected to the inputs of the second adders of unquantized variations of the integral with respect to the first and second coordinates, respectively, “the output of the integral remainder register is connected to the inputs of the second addendum summers of the remainder of the vari able integral lp in the first and second coordinates, the outputs i of which are connected to the second inputs of the first and second elements AND, the integrator clock signals are connected to the synchronization inputs of the first and second registers of unquantized 35 45 variations of the integrape.