Numerical analysis device and numerical analysis program

Abstract

A second derivative of a second-order differential equation is calculated at a reference variable value. The second derivative is multiplied by an analytical small variable value, the first derivative at the reference variable value is added, and a result is output as a first derivative after an increment of the analytical small variable value. The first derivative after an increment of the analytical small variable value is multiplied by the analytical small variable value, a physical value at the reference variable value is added, and a result is output as a physical value after an increment of the analytical small variable value.

1 - 36 . (canceled) 
   
   
       37 . A numerical analysis device that performs a numerical analysis of second-order differential equation for a target object to be analyzed, the numerical analysis device comprising:
 a setting unit that performs a setting of parameters including an initial condition of the second-order differential equation and a setting of an analytical small variable value for the numerical analysis;   a second-derivative calculation unit that calculates a second derivative of the second-order differential equation at a reference variable value that is a variable at the start of the numerical analysis;   a first-derivative calculation unit that performs a multiplication of the second derivative calculated by the second-derivative calculation unit by the analytical small variable value and an addition of the first derivative of the second-order differential equation at the reference variable value to a value obtained by the multiplication, and outputs a value obtained by the addition as a first derivative after an increment of the analytical small variable value;   a physical-value calculation unit that performs a multiplication of the first derivative calculated by the first-derivative calculation unit by the analytical small variable value and an addition of a physical value of the second-order differential equation at the reference variable value to a value obtained by the multiplication, and outputs a value obtained by the addition as a physical value after an increment of the analytical small variable value; and   an operation control unit that repeats a control of setting a variable value obtained by adding the analytical small variable value to the reference variable value as a new reference variable value and causing the second-derivative calculation unit, the first-derivative calculation unit, and the physical-value calculation unit to calculate the second derivative, the first derivative, and the physical value, using the new reference variable value, respectively.   
   
   
       38 . The numerical analysis device according to  claim 37 , wherein
 the analytical small variable value and the reference variable value are an analytical small time and reference time, respectively, and   the first derivative and the second derivative are a first-order time derivative and a second-order time derivative, respectively.   
   
   
       39 . The numerical analysis device according to  claim 37 , wherein
 the setting unit sets a termination condition of the numerical analysis, and   when the termination condition of the numerical analysis is satisfied, the operation control unit performs a control of terminating the numerical analysis.   
   
   
       40 . The numerical analysis device according to  claim 37 , further comprising an output processing unit that outputs the physical value of each reference variable value calculated by the physical-value calculation unit, in association with the increment of the analytical small variable value. 
   
   
       41 . The numerical analysis device according to  claim 40 , wherein the output processing unit generates a graph of the physical value for each reference variable value calculated by the physical-value calculation unit corresponding to the increment of the analytical small variable value. 
   
   
       42 . The numerical analysis device according to  claim 37 , wherein the second-order differential equation includes a variable value term. 
   
   
       43 . The numerical analysis device according to  claim 38 , wherein the second-order differential equation includes a time term. 
   
   
       44 . The numerical analysis device according to  claim 37 , wherein the second-order differential equation is a simultaneous equation with multiple unknowns. 
   
   
       45 . The numerical analysis device according to  claim 37 , wherein the numerical analysis is performed using a spreadsheet program. 
   
   
       46 . A numerical analysis device that performs a numerical analysis of second-order differential equation for a target object to be analyzed, the numerical analysis device comprising:
 a setting unit that performs a setting of parameters including an initial condition of the second-order differential equation and a setting of an analytical small variable value for the numerical analysis;   a second-derivative calculation unit that calculates a second derivative of the second-order differential equation at a reference variable value that is a variable at the start of the numerical analysis;   a first-derivative calculation unit that performs a multiplication of the second derivative calculated by the second-derivative calculation unit by the analytical small variable value and an addition of the first derivative of the second-order differential equation at the reference variable value to a value obtained by the multiplication, and outputs a value obtained by the addition as a first derivative after an increment of the analytical small variable value;   a physical-value calculation unit that performs a multiplication of the second derivative calculated by the second-derivative calculation unit by a square value of the analytical small variable value, a multiplication of the first derivative calculated by the first-derivative calculation unit by the analytical small variable value, and an addition of values obtained by the multiplications and a physical value of the second-order differential equation at the reference variable value, and outputs a value obtained by the addition as a physical value after an increment of the analytical small variable value; and   an operation control unit that repeats a control of setting a variable value obtained by adding the analytical small variable value to the reference variable value as a new reference variable value and causing the second-derivative calculation unit, the first-derivative calculation unit, and the physical-value calculation unit to calculate the second derivative, the first derivative, and the physical value, using the new reference variable value, respectively.   
   
   
       47 . The numerical analysis device according to  claim 46 , wherein
 the analytical small variable value and the reference variable value are an analytical small time and reference time, respectively, and   the first derivative and the second derivative are a first-order time derivative and a second-order time derivative, respectively.   
   
   
       48 . The numerical analysis device according to  claim 46 , wherein
 the setting unit sets a termination condition of the numerical analysis, and   when the termination condition of the numerical analysis is satisfied, the operation control unit performs a control of terminating the numerical analysis.   
   
   
       49 . The numerical analysis device according to  claim 46 , further comprising an output processing unit that outputs the physical value of each reference variable value calculated by the physical-value calculation unit, in association with the increment of the analytical small variable value. 
   
   
       50 . The numerical analysis device according to  claim 49 , wherein the output processing unit generates a graph of the physical value for each reference variable value calculated by the physical-value calculation unit corresponding to the increment of the analytical small variable value. 
   
   
       51 . The numerical analysis device according to  claim 46 , wherein the second-order differential equation includes a variable value term. 
   
   
       52 . The numerical analysis device according to  claim 47 , wherein the second-order differential equation includes a time term. 
   
   
       53 . The numerical analysis device according to  claim 46 , wherein the second-order differential equation is a simultaneous equation with multiple unknowns. 
   
   
       54 . The numerical analysis device according to  claim 46 , wherein the numerical analysis is performed using a spreadsheet program. 
   
   
       55 . A computer-readable recording medium that stores therein a numerical analysis program for a numerical analysis of second-order differential equation for a target object to be analyzed, the numerical analysis program causing a computer to execute:
 parameter setting including performing a setting of parameters including an initial condition of the second-order differential equation and a setting of an analytical small variable value for the numerical analysis;   second-derivative calculating including calculating a second derivative of the second-order differential equation at a reference variable value that is a variable at the start of the numerical analysis;   first-derivative calculating including
 performing a multiplication of the second derivative calculated at the second-derivative calculating by the analytical small variable value and an addition of the first derivative of the second-order differential equation at the reference variable value to a value obtained by the multiplication, and 
 outputting a value obtained by the addition as a first derivative after an increment of the analytical small variable value; 
   physical-value calculating including
 performing a multiplication of the first derivative calculated at the first-derivative calculating by the analytical small variable value and an addition of a physical value of the second-order differential equation at the reference variable value to a value obtained by the multiplication, and 
 outputting a value obtained by the addition as a physical value after an increment of the analytical small variable value; and 
   operation controlling including repeating a control of
 setting a variable value obtained by adding the analytical small variable value to the reference variable value as a new reference variable value, and 
 causing the second-derivative calculating, the first-derivative calculating, and the physical-value calculating to calculate the second derivative, the first derivative, and the physical value, using the new reference variable value, respectively. 
   
   
   
       56 . The computer-readable recording medium according to  claim 55 , wherein
 the analytical small variable value and the reference variable value are an analytical small time and reference time, respectively, and   the first derivative and the second derivative are a first-order time derivative and a second-order time derivative, respectively.   
   
   
       57 . The computer-readable recording medium according to  claim 55 , wherein
 the parameter setting includes setting a termination condition of the numerical analysis, and   when the termination condition of the numerical analysis is satisfied, the operation controlling includes performing a control of terminating the numerical analysis.   
   
   
       58 . The computer-readable recording medium according to  claim 55 , wherein the numerical analysis program further causes the computer to execute output processing including outputting the physical value of each reference variable value calculated at the physical-value calculating, in association with the increment of the analytical small variable value. 
   
   
       59 . The computer-readable recording medium according to  claim 58 , wherein the output processing includes generating a graph of the physical value for each reference variable value calculated at the physical-value calculating corresponding to the increment of the analytical small variable value. 
   
   
       60 . The computer-readable recording medium according to  claim 55 , wherein the second-order differential equation includes a variable value term. 
   
   
       61 . The computer-readable recording medium according to  claim 56 , wherein the second-order differential equation includes a time term. 
   
   
       62 . The computer-readable recording medium according to  claim 55 , wherein the second-order differential equation is a simultaneous equation with multiple unknowns. 
   
   
       63 . The computer-readable recording medium according to  claim 55 , wherein the numerical analysis is performed using a spreadsheet program. 
   
   
       64 . A computer-readable recording medium that stores therein a numerical analysis program for a numerical analysis of second-order differential equation for a target object to be analyzed, the numerical analysis program causing a computer to execute:
 parameter setting including performing a setting of parameters including an initial condition of the second-order differential equation and a setting of an analytical small variable value for the numerical analysis;   second-derivative calculating including calculating a second derivative of the second-order differential equation at a reference variable value that is a variable at the start of the numerical analysis;   first-derivative calculating including performing a multiplication of the second derivative calculated at the second-derivative calculating by the analytical small variable value and an addition of the first derivative of the second-order differential equation at the reference variable value to a value obtained by the multiplication, and outputting a value obtained by the addition as a first derivative after an increment of the analytical small variable value;   physical-value calculating including performing a multiplication of the second derivative calculated at the second-derivative calculating by a square value of the analytical small variable value, a multiplication of the first derivative calculated at the first-derivative calculating by the analytical small variable value, and an addition of values obtained by the multiplications and a physical value of the second-order differential equation at the reference variable value, and outputting a value obtained by the addition as a physical value after an increment of the analytical small variable value; and   operation controlling including repeating a control of
 setting a variable value obtained by adding the analytical small variable value to the reference variable value as a new reference variable value, and 
 causing the second-derivative calculating, the first-derivative calculating, and the physical-value calculating to calculate the second derivative, the first derivative, and the physical value, using the new reference variable value, respectively. 
   
   
   
       65 . The computer-readable recording medium according to  claim 64 , wherein
 the analytical small variable value and the reference variable value are an analytical small time and reference time, respectively, and   the first derivative and the second derivative are a first-order time derivative and a second-order time derivative, respectively.   
   
   
       66 . The computer-readable recording medium according to  claim 64 , wherein
 the parameter setting includes setting a termination condition of the numerical analysis, and   when the termination condition of the numerical analysis is satisfied, the operation controlling includes performing a control of terminating the numerical analysis.   
   
   
       67 . The computer-readable recording medium according to  claim 64 , wherein the numerical analysis program further causes the computer to execute output processing including outputting the physical value of each reference variable value calculated at the physical-value calculating, in association with the increment of the analytical small variable value. 
   
   
       68 . The computer-readable recording medium according to  claim 67 , wherein the output processing includes generating a graph of the physical value for each reference variable value calculated at the physical-value calculating corresponding to the increment of the analytical small variable value. 
   
   
       69 . The computer-readable recording medium according to  claim 64 , wherein the second-order differential equation includes a variable value term. 
   
   
       70 . The computer-readable recording medium according to  claim 65 , wherein the second-order differential equation includes a time term. 
   
   
       71 . The computer-readable recording medium according to  claim 64 , wherein the second-order differential equation is a simultaneous equation with multiple unknowns. 
   
   
       72 . The computer-readable recording medium according to  claim 64 , wherein the numerical analysis is performed using a spreadsheet program.