text: fig1 shows a configuration of an information output method of the present invention . in the present method , there are four input data . the first is shape data 13 representing a shape of an analysis domain , the second is mesh point coordinate data representing coordinates of mesh points which are representative points of the analysis domain , the third one is discretion reference data 11 representing a reference relation of the mesh points in the discretization equations , and the fourth is coefficient / constant data 12 representing a coefficient matrix and a constant matrix of the simultaneous linear equations constructed by the discretization equations of the field equations ( partial differential equations and boundary condition equations ). one of the outputs of the present method is an output fig1 drawn at the position of the mesh point in the analysis domain , which represents analog information indicating ratios of coefficients and constants representing the nature of the discretization equations and the discretion reference relation . another output in the present method is an output 20 which indicates a position of a mesh point to be additionally provided for amendment . the present method comprises the following three parts . the first part is to generate output data 14 . for each mesh point , a relative position ( angle ) of the discretion reference point to the mesh point is determined ( 151 ), and then a ratio of coefficients of the discretion reference point and the mesh point is determined ( 152 ) to generate the output data 16 . the second part is to output analog data 17 . the output data 16 is converted to analog data represented by a polygonal shape , size and color for each mesh point , and it is drawn at the position of the mesh point , in the analysis domain . the third part is to generate amendment data 19 . the output data 16 having a large ratio of coefficients is selected for coordinates of an intermediate point between the mesh point and the reference point related to the large coefficient ratio and are outputted as a mesh point to be newly provided . the present embodiment is explained in detail . the data 10 , 11 , 12 , 13 , 16 , 18 and 20 are explained in detail , and then the parts 14 , 17 and 19 are explained in detail . the input information 10 , 11 and 12 are shown in fig5 which corresponds to fig2 - 4 . numeral 51 denotes an analysis domain and mesh points p 1 - p 9 which have coordinates ( x 0 , y 0 , z 0 ) . . . broken lines represent discretion reference relations . the mesh point coordinate data 10 represents spatial coordinates of the mesh points . each mesh point has x , y and z coordinates . for example , information 51 that the coordinates of the mesh point p 0 is ( x 0 , y 0 , z 0 ) is inputted in the form of 10 of fig5 . the discretion reference data 11 indicates the discretion reference relation of the discretization equation for each mesh point . for example , the discretion reference points for the mesh point p 2 are four points p 0 , p 1 , p 3 and p 4 as shown by broken lines in 51 , and those four points and the point p 2 are registered in the column p 2 of the data 11 which show the discretion reference relation . the coefficient / constant data 12 comprises coefficient data 52 and constant data 53 . it holds coefficients and constants of the simultaneous linear equations constructed by the discretization equations at the respective mesh points . the coefficient data 52 correspond to the discretion reference data . for example , when au p0 + bu p1 + cu p2 + du p3 + eu p4 = con 2 ( where u pn is an unknown at point p n and con 2 is a constant ), the data 11 and 12 are generated . the mesh points in the mesh point coordinate data 10 , the discretion reference data 11 and the coefficient / constant data 12 are arranged in the same order / vertical arrangement p 0 , p 1 , . . . in the tables of fig5 ). as other input information , shape data 13 ( fig1 ) holds data representing the shape of the analysis domain in the form of coordinates . the output fig1 of the output information is now explained with reference to fig6 . numeral 18 denotes the output figure , and 61 and 63 are shown for explanation purposes . the analysis domain , mesh points and the reference relation thereof are shown by 61 . the output figure for 61 is shown by 18 in which polygons on the mesh points ( shown by dots ) and a symbol x represent the nature of the discretization equations . the words &# 34 ; nature of a discretization equation &# 34 ; mean whether such discretization equation is easy to solve via numerical analysis or not . the nature is determined by a position at which a non - zero coefficient appears in the coefficient matrix and a magnitude of the non - zero coefficient . polygons on each mesh point and a symbol x represent a position at which a non - zero coefficient appears in the coefficient matrix . the details are as follows . the meaning of the polygons is explained with reference to 63 and 64 . looking at the point p 2 , the discretion reference points are p 0 , p 3 and p 4 . the discretization equation au p0 + bu p1 + cu p2 + du p3 + eu p4 = con 2 ( 64 ) is satisfied , where u is an unknown , a - e are coefficients and con 2 is a constant . it is important for the operator to understand the nature of matrix such as positions of the discretion reference points at each mesh point , ratios of coefficients of the discretion reference points , and ratios of the constants . in the present embodiment , they are outputted . assuming that the symbols x in 63 represent mesh points , vertexes of the polygon are on lines connecting the mesh point p 2 and the discretion reference points p 0 , p 1 , p 3 and p 4 . the lengths from the point p 2 to the vertexes are represented by absolute values of ratios of the coefficients of the point p 2 and the discretion reference points . the color and brightness of the polygon are changed depending on the coefficient of the mesh point and the constants of the discretization equations . if the coefficient of the mesh point in the at a position corresponding to the point p 8 as shown in fig6 b . the output data ( 16 in fig1 ) which is the intermediate information is shown in fig7 . it is numerical data 16 corresponding to the output fig1 of fig6 b . for each mesh point , the coordinates , angles of discretion reference points , coefficient ratios and constant ratios are held . the angle is one for the discretion reference point with the mesh point being an origin point . for example the angle of the discretion reference point p 4 at the mesh point p 2 is θ 4 , as shown by 72 . the coefficient ratio is a quotient of the coefficient of the discretion reference point divided by the coefficient of the mesh point . the sequence of vertically arranged mesh points and the sequence of horizontally arranged discretion reference points of the data table 16 are same as the sequences of the discretion reference data 11 and the coefficient / constant data 12 of fig5 . the horizontally arranged discretion reference points include a column to indicate the corresponding mesh point . in the output data , the data column indicating the angle is blank . the data column indicating the coefficient ratio is always &# 34 ; 1 &# 34 ; . if the coefficient at the mesh point is zero , the data column indicating the coefficient ratio is &# 34 ;- 1 &# 34 ; and the data column indicating the coefficient ratio to other discretion reference points is blank . the amendment data 20 which is further output information is explained . it is a mesh point to be newly added when the nature of the discretization equations is poor . the coordinates thereof are outputted sequentially from the top of the screen . the output data generation step 14 of fig1 is explained . in this step , the mesh point coordinate data 10 , the discretion reference data 11 and the coefficient / constant data 12 of fig5 are inputs and the output data 16 of fig7 is an output . a flow chart thereof is shown in fig8 . the following steps are carried out for each mesh point in the analysis domain ( 80 ). the coefficient of the mesh point in the discretization equation is looked up based on the discretion reference data and the coefficient / constant data 12 ( fig1 and 5 ) ( 81 ). if the looked - up coefficient is zero ( 82 ), the column in the output data 16 ( fig1 and 7 ) which indicates the coefficient ratio of the mesh points is set to &# 34 ;- 1 &# 34 ; ( 83 ). if the coefficient is not zero , the following step is carried out ( 82 ). for each discretion reference point in the discretization equation for the mesh point ( 84 ), the position ( angle ) of the discretion reference point relative to the mesh point is determined based on the mesh point coordinate data 10 and the discretion reference data 11 ( 72 in fig7 ), and it is entered into the output data 16 ( 85 ). then , a quotient of the coefficient of the discretion reference point divided by the coefficient of the mesh point is calculated based on the discretion reference data 11 and the coefficient / constant data 52 , and the ratio thereof is entered into the output data 16 ( 86 ). a quotient of the constant divided by the coefficient of the mesh point is calculated based on the coefficient / constant data 12 , and the ratio thereof is entered into the output data 16 ( 87 ). the above is the flow of the output data generation step 14 . the analog data output step 17 of fig1 is now explained . in the analog data generation step 17 , the shape data 13 and the output data 16 of fig7 are inputs and the output fig1 of fig6 is an output . the shape of the analysis domain is outputted from the shape data . for each mesh point , a polygon having vertexes at points of the lengths of coefficient ratio in the direction toward the discretion reference points is drawn at the corresponding mesh point in the analysis domain . the point having the coefficient ratio of mesh points of &# 34 ;- 1 &# 34 ; in the output data 16 is indicates by a symbol x . the constant ratio is represented by a density of color of the polygon . finally , the amendment data generation step 19 of fig1 is explained . in the amendment data generation step 19 , the output data 16 of fig7 is an input and the amendment data 20 of fig1 which indicates the mesh point to be newly provided is an output . the steps are shown in fig9 . for each mesh point , the following step is carried out ( 91 ). reference points for the mesh point are determined based on the output data 16 ( 92 ). for each reference point , the following step is carried out ( 93 ). the column &# 34 ; coefficient ratio &# 34 ; in the output data 16 is referred to determine if it is larger than 1 or not ( 94 ). if it is larger , coordinates of an intermediate point between the mesh point and the reference point are determined ( 95 ). the coordinates are supplied to the amendment data 20 as the output of the amendment data generation step 19 and displayed as newly required coordinates . in accordance with the present embodiment , the coefficient ratios and constant ratios at the mesh points in the analysis domain are visually indicated . accordingly , a cause of error of program and a defect of the model for the discretization equation having a large variety of coefficient ratios can be readily identified . in the present embodiment , the coefficient ratios and the constant ratios are outputted . alternatively , the equal equations in the simultaneous linear equations may be detected and the mesh point thereof may be outputted , or other information on the discretization equations may be outputted . the information in the course of solution of the matrix may also be outputted . the output forms may be shape , color and size of the marker , or vector chart or animation . the input data may be simultaneous linear equations , conventional discretization equations or known coefficients . in accordance with the present embodiment , the mesh point to be added when numerical error has occurred is indicated . accordingly , the amendment of the program is facilitated . in accordance with the present invention , the data representing the nature of the discretization equations which are approximation equations of the partial differential equations is converted to analog data such as size , shape and color of the marker and graphically outputted at the positions corresponding to the mesh points in the analysis domain . accordingly , the following advantages are presented . when the operator solves the partial differential equation in a numerical analysis manner , he / she can comprehend the nature of the discretization equation without directly watching the numeric data . accordingly , the defect in the model and the cause of error in the program can be readily detected and the efficiency in developing the numerical simulation program is improved . in accordance with the present invention , the coordinates of the mesh point to be newly provided are outputted . accordingly , the operator without knowledge of physical models and numerical analysis can readily amend the program , and efficiency in developing the numerical simulation program is improved .